diff --git a/graph/edmonds_karp.ts b/graph/edmonds_karp.ts
new file mode 100644
index 00000000..fb781a42
--- /dev/null
+++ b/graph/edmonds_karp.ts
@@ -0,0 +1,97 @@
+import { StackQueue } from '../data_structures/queue/stack_queue'
+
+/**
+ * @function edmondsKarp
+ * @description Compute the maximum flow from a source node to a sink node using the Edmonds-Karp algorithm.
+ * @Complexity_Analysis
+ * Time complexity: O(V * E^2) where V is the number of vertices and E is the number of edges.
+ * Space Complexity: O(E) due to residual graph representation.
+ * @param {[number, number][][]} graph - The graph in adjacency list form.
+ * @param {number} source - The source node.
+ * @param {number} sink - The sink node.
+ * @return {number} - The maximum flow from the source node to the sink node.
+ * @see https://en.wikipedia.org/wiki/Edmonds%E2%80%93Karp_algorithm
+ */
+export default function edmondsKarp(
+  graph: [number, number][][],
+  source: number,
+  sink: number
+): number {
+  const n = graph.length
+
+  // Initialize residual graph
+  const residualGraph: [number, number][][] = Array.from(
+    { length: n },
+    () => []
+  )
+
+  // Build residual graph from the original graph
+  for (let u = 0; u < n; u++) {
+    for (const [v, cap] of graph[u]) {
+      if (cap > 0) {
+        residualGraph[u].push([v, cap]) // Forward edge
+        residualGraph[v].push([u, 0]) // Reverse edge with 0 capacity
+      }
+    }
+  }
+
+  const findAugmentingPath = (parent: (number | null)[]): number => {
+    const visited = Array(n).fill(false)
+    const queue = new StackQueue<number>()
+    queue.enqueue(source)
+    visited[source] = true
+    parent[source] = null
+
+    while (queue.length() > 0) {
+      const u = queue.dequeue()
+      for (const [v, cap] of residualGraph[u]) {
+        if (!visited[v] && cap > 0) {
+          parent[v] = u
+          visited[v] = true
+          if (v === sink) {
+            // Return the bottleneck capacity along the path
+            let pathFlow = Infinity
+            let current = v
+            while (parent[current] !== null) {
+              const prev = parent[current]!
+              const edgeCap = residualGraph[prev].find(
+                ([node]) => node === current
+              )![1]
+              pathFlow = Math.min(pathFlow, edgeCap)
+              current = prev
+            }
+            return pathFlow
+          }
+          queue.enqueue(v)
+        }
+      }
+    }
+    return 0
+  }
+
+  let maxFlow = 0
+  const parent = Array(n).fill(null)
+
+  while (true) {
+    const pathFlow = findAugmentingPath(parent)
+    if (pathFlow === 0) break // No augmenting path found
+
+    // Update the capacities and reverse capacities in the residual graph
+    let v = sink
+    while (parent[v] !== null) {
+      const u = parent[v]!
+      // Update capacity of the forward edge
+      const forwardEdge = residualGraph[u].find(([node]) => node === v)!
+      forwardEdge[1] -= pathFlow
+      // Update capacity of the reverse edge
+      const reverseEdge = residualGraph[v].find(([node]) => node === u)!
+      reverseEdge[1] += pathFlow
+
+      v = u
+    }
+
+    maxFlow += pathFlow
+  }
+
+  return maxFlow
+}
diff --git a/graph/test/edmonds_karp.test.ts b/graph/test/edmonds_karp.test.ts
new file mode 100644
index 00000000..22711ab9
--- /dev/null
+++ b/graph/test/edmonds_karp.test.ts
@@ -0,0 +1,82 @@
+import edmondsKarp from '../edmonds_karp'
+
+describe('Edmonds-Karp Algorithm', () => {
+  it('should find the maximum flow in a simple graph', () => {
+    const graph: [number, number][][] = [
+      [
+        [1, 3],
+        [2, 2]
+      ], // Node 0: Edges to node 1 (capacity 3), and node 2 (capacity 2)
+      [[3, 2]], // Node 1: Edge to node 3 (capacity 2)
+      [[3, 3]], // Node 2: Edge to node 3 (capacity 3)
+      [] // Node 3: No outgoing edges
+    ]
+    const source = 0
+    const sink = 3
+    const maxFlow = edmondsKarp(graph, source, sink)
+    expect(maxFlow).toBe(4)
+  })
+
+  it('should find the maximum flow in a more complex graph', () => {
+    const graph: [number, number][][] = [
+      [
+        [1, 10],
+        [2, 10]
+      ], // Node 0: Edges to node 1 and node 2 (both capacity 10)
+      [
+        [3, 4],
+        [4, 8]
+      ], // Node 1: Edges to node 3 (capacity 4), and node 4 (capacity 8)
+      [[4, 9]], // Node 2: Edge to node 4 (capacity 9)
+      [[5, 10]], // Node 3: Edge to node 5 (capacity 10)
+      [[5, 10]], // Node 4: Edge to node 5 (capacity 10)
+      [] // Node 5: No outgoing edges (sink)
+    ]
+    const source = 0
+    const sink = 5
+    const maxFlow = edmondsKarp(graph, source, sink)
+    expect(maxFlow).toBe(14)
+  })
+
+  it('should return 0 when there is no path from source to sink', () => {
+    const graph: [number, number][][] = [
+      [], // Node 0: No outgoing edges
+      [], // Node 1: No outgoing edges
+      [] // Node 2: No outgoing edges (sink)
+    ]
+    const source = 0
+    const sink = 2
+    const maxFlow = edmondsKarp(graph, source, sink)
+    expect(maxFlow).toBe(0)
+  })
+
+  it('should handle graphs with no edges', () => {
+    const graph: [number, number][][] = [
+      [], // Node 0: No outgoing edges
+      [], // Node 1: No outgoing edges
+      [] // Node 2: No outgoing edges
+    ]
+    const source = 0
+    const sink = 2
+    const maxFlow = edmondsKarp(graph, source, sink)
+    expect(maxFlow).toBe(0)
+  })
+
+  it('should handle graphs with self-loops', () => {
+    const graph: [number, number][][] = [
+      [
+        [0, 10],
+        [1, 10]
+      ], // Node 0: Self-loop with capacity 10, and edge to node 1 (capacity 10)
+      [
+        [1, 10],
+        [2, 10]
+      ], // Node 1: Self-loop and edge to node 2
+      [] // Node 2: No outgoing edges (sink)
+    ]
+    const source = 0
+    const sink = 2
+    const maxFlow = edmondsKarp(graph, source, sink)
+    expect(maxFlow).toBe(10)
+  })
+})
diff --git a/search/binary_search.ts b/search/binary_search.ts
index 39d380a4..cf86f39a 100644
--- a/search/binary_search.ts
+++ b/search/binary_search.ts
@@ -8,25 +8,25 @@
  *
  * @param {number[]} array - sorted list of numbers
  * @param {number} target - target number to search for
- * @return {number} - index of the target number in the list, or -1 if not found
+ * @return {number} - index of the target number in the list, or null if not found
  * @see [BinarySearch](https://www.geeksforgeeks.org/binary-search/)
  * @example binarySearch([1,2,3], 2) => 1
- * @example binarySearch([4,5,6], 2) => -1
+ * @example binarySearch([4,5,6], 2) => null
  */
 
 export const binarySearchIterative = (
   array: number[],
-  target: number
-): number => {
-  if (array.length === 0) return -1
-
-  // declare pointers for the start, middle and end indices
-  let start = 0,
-    end = array.length - 1,
-    middle = (start + end) >> 1
+  target: number,
+  start: number = 0,
+  end: number = array.length - 1
+): number | null => {
+  if (array.length === 0) return null
 
   // ensure the target is within the bounds of the array
-  if (target < array[start] || target > array[end]) return -1
+  if (target < array[start] || target > array[end]) return null
+
+  // declare pointers for the middle index
+  let middle = (start + end) >> 1
 
   while (array[middle] !== target && start <= end) {
     // if the target is less than the middle value, move the end pointer to be middle -1 to narrow the search space
@@ -37,7 +37,7 @@ export const binarySearchIterative = (
     middle = (start + end) >> 1
   }
   // return the middle index if it is equal to target
-  return array[middle] === target ? middle : -1
+  return array[middle] === target ? middle : null
 }
 
 export const binarySearchRecursive = (
@@ -45,16 +45,16 @@ export const binarySearchRecursive = (
   target: number,
   start = 0,
   end = array.length - 1
-): number => {
-  if (array.length === 0) return -1
+): number | null => {
+  if (array.length === 0) return null
 
   // ensure the target is within the bounds of the array
-  if (target < array[start] || target > array[end]) return -1
+  if (target < array[start] || target > array[end]) return null
 
   const middle = (start + end) >> 1
 
   if (array[middle] === target) return middle // target found
-  if (start > end) return -1 // target not found
+  if (start > end) return null // target not found
 
   // if the target is less than the middle value, move the end pointer to be middle -1 to narrow the search space
   // otherwise, move the start pointer to be middle + 1
diff --git a/search/exponential_search.ts b/search/exponential_search.ts
new file mode 100644
index 00000000..4a8eba47
--- /dev/null
+++ b/search/exponential_search.ts
@@ -0,0 +1,40 @@
+import { binarySearchIterative } from './binary_search'
+
+/**
+ * @description Exponential search algorithm for a sorted array.
+ *
+ * The algorithm searches for a specific value in a sorted array by first finding a range
+ * where the value may be present and then performing a binary search within that range.
+ *
+ * Compared with binary search, exponential search can be more convenient and advantageous
+ * in cases where the element to be searched is closer to the beginning of the array,
+ * thus avoiding several comparisons that would make the search more verbose.
+ *
+ * @param {number[]} array - sorted list of numbers
+ * @param {number} x - target number to search for
+ * @return {number | null} - index of the target number in the list, or null if not found
+ * @see [ExponentialSearch](https://www.geeksforgeeks.org/exponential-search/)
+ * @example exponentialSearch([1, 2, 3, 4, 5], 3) => 2
+ * @example exponentialSearch([10, 20, 30, 40, 50], 35) => null
+ */
+
+export const exponentialSearch = (
+  array: number[],
+  x: number
+): number | null => {
+  const arrayLength = array.length
+  if (arrayLength === 0) return null
+
+  if (array[0] === x) return 0
+
+  let i = 1
+  while (i < arrayLength && array[i] <= x) {
+    i = i * 2
+  }
+
+  const start = Math.floor(i / 2)
+  const end = Math.min(i, arrayLength - 1)
+  const result = binarySearchIterative(array, x, start, end)
+
+  return result
+}
diff --git a/search/fibonacci_search.ts b/search/fibonacci_search.ts
new file mode 100644
index 00000000..b0125277
--- /dev/null
+++ b/search/fibonacci_search.ts
@@ -0,0 +1,57 @@
+/**
+ * @description Fibonacci search algorithm for a sorted array.
+ *
+ * The algorithm searches for a specific value in a sorted array using Fibonacci numbers
+ * to divide the array into smaller subarrays. This algorithm is useful for large arrays where
+ * the cost of accessing elements is high.
+ *
+ * @param {number[]} array - sorted list of numbers
+ * @param {number} target - target number to search for
+ * @return {number | null} - index of the target number in the list, or null if not found
+ * @see [FibonacciSearch](https://www.geeksforgeeks.org/fibonacci-search/)
+ * @example fibonacciSearch([1,2,3], 2) => 1
+ * @example fibonacciSearch([4,5,6], 2) => null
+ */
+
+export const fibonacciSearch = (
+  array: number[],
+  target: number
+): number | null => {
+  const arrayLength = array.length
+  let a = 0 // (n-2)'th Fibonacci No.
+  let b = 1 // (n-1)'th Fibonacci No.
+  let c = a + b // n'th Fibonacci
+
+  while (c < arrayLength) {
+    a = b
+    b = c
+    c = a + b
+  }
+
+  let offset = -1
+
+  while (c > 1) {
+    let i = Math.min(offset + a, arrayLength - 1)
+
+    if (array[i] < target) {
+      c = b
+      b = a
+      a = c - b
+      offset = i
+    } else if (array[i] > target) {
+      c = a
+      b = b - a
+      a = c - b
+    } else {
+      // Element found then return index
+      return i
+    }
+  }
+
+  if (b && array[offset + 1] === target) {
+    return offset + 1
+  }
+
+  // Element not found then return null
+  return null
+}
diff --git a/search/test/binary_search.test.ts b/search/test/binary_search.test.ts
index 6ebd12d9..13b13251 100644
--- a/search/test/binary_search.test.ts
+++ b/search/test/binary_search.test.ts
@@ -2,7 +2,7 @@ import { binarySearchIterative, binarySearchRecursive } from '../binary_search'
 
 describe('BinarySearch', () => {
   const testArray: number[] = [1, 2, 3, 4]
-  type FunctionsArray = { (array: number[], index: number): number }[]
+  type FunctionsArray = { (array: number[], index: number): number | null }[]
   const functions: FunctionsArray = [
     binarySearchIterative,
     binarySearchRecursive
@@ -12,14 +12,16 @@ describe('BinarySearch', () => {
     it('should be defined', () => {
       expect(func(testArray, 2)).toBeDefined()
     })
-    it('should return a number', () => {
-      expect(typeof func(testArray, 2)).toBe('number')
+    it('should return a number or null', () => {
+      expect(
+        typeof func(testArray, 2) === 'number' || func(testArray, 2) === null
+      ).toBe(true)
     })
-    it('should return -1 if the target is not found in the array', () => {
-      expect(func(testArray, 5)).toBe(-1)
+    it('should return null if the target is not found in the array', () => {
+      expect(func(testArray, 5)).toBe(null)
     })
-    it('should return -1 if there are no elements in the array', () => {
-      expect(func([], 5)).toBe(-1)
+    it('should return null if there are no elements in the array', () => {
+      expect(func([], 5)).toBe(null)
     })
     it('should return the index of the target if it is found in the array', () => {
       expect(func(testArray, 2)).toBe(1)
diff --git a/search/test/exponential_search.test.ts b/search/test/exponential_search.test.ts
new file mode 100644
index 00000000..80f6a07f
--- /dev/null
+++ b/search/test/exponential_search.test.ts
@@ -0,0 +1,19 @@
+import { exponentialSearch } from '../exponential_search'
+
+describe('Exponential search', () => {
+  test.each([
+    [[1, 2, 3, 4, 5], 3, 2],
+    [[10, 20, 30, 40, 50], 35, null],
+    [[10, 20, 30, 40, 50], 10, 0],
+    [[10, 20, 30, 40, 50], 50, 4],
+    [[10, 20, 30, 40, 50], 60, null],
+    [[], 10, null],
+    [[1, 2, 3, 4, 5], 1, 0],
+    [[1, 2, 3, 4, 5], 5, 4]
+  ])(
+    'of %o, searching for %o, expected %i',
+    (array: number[], target: number, expected: number | null) => {
+      expect(exponentialSearch(array, target)).toBe(expected)
+    }
+  )
+})
diff --git a/search/test/fibonacci_search.test.ts b/search/test/fibonacci_search.test.ts
new file mode 100644
index 00000000..5b2b54b7
--- /dev/null
+++ b/search/test/fibonacci_search.test.ts
@@ -0,0 +1,18 @@
+import { fibonacciSearch } from '../fibonacci_search'
+
+describe('Fibonacci search', () => {
+  test.each([
+    [[1, 2, 3], 2, 1],
+    [[4, 5, 6], 2, null],
+    [[10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100], 85, 8],
+    [[], 1, null],
+    [[1], 1, 0],
+    [[1, 3, 5, 7, 9, 11, 13], 11, 5],
+    [[1, 3, 5, 7, 9, 11, 13], 8, null]
+  ])(
+    'of %o, searching for %o, expected %i',
+    (array: number[], target: number, expected: number | null) => {
+      expect(fibonacciSearch(array, target)).toBe(expected)
+    }
+  )
+})