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How many minimum edges in a Cyclic graph with n vertices?
The term "cyclic graph" is not well-defined. If you mean a graph that is not acyclic, then the answer is 3. That would be the union of a complete graph on 3 vertices and any number of isolated vertices. If you mean a graph that is (isomorphic to) a cycle, then the answer is n. If you are really asking the maximum number of edges, then that would be the triangle numbers such as n (n-1) /2.
Prove that every tree with two or more vertices is bichromatic?
Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.
How many subgraphs with at least one vertex does a complete graph of 3 vertices k3 have?
one vertex: 3 two vertices: 6 three vertices: 8 total 17
The minimum number of edges in a connected cyclic graph on n vertices is?
n-1
What is the maximum number of edges in an undirected graph with V vertices?
V*(V-1)/2
What is the relationship between Dijkstra's algorithm and breadth-first search in graph traversal?
Dijkstra's algorithm is a more advanced version of breadth-first search in graph traversal. While both algorithms explore nodes in a graph, Dijkstra's algorithm considers the weight of edges to find the shortest path, whereas breadth-first search simply explores nodes in a level-by-level manner.
How can you design an algorithm to check if a given graph is connected?
Use a simple DFS/BFS traversal. If you have gone through all nodes, the graph is connected.
What is the space complexity of the Dijkstra algorithm?
The space complexity of the Dijkstra algorithm is O(V), where V is the number of vertices in the graph.
What is the average running time of Dijkstra's algorithm for finding the shortest path in a graph?
The average running time of Dijkstra's algorithm for finding the shortest path in a graph is O(V2), where V is the number of vertices in the graph.
In depth first traversal of a graph G with n vertices k edges are marked as tree edges the no of connected components in G is?
n-k-1
What is the runtime complexity of Kruskal's algorithm for finding the minimum spanning tree of a graph?
The runtime complexity of Kruskal's algorithm is O(E log V), where E is the number of edges and V is the number of vertices in the graph.
What is welch powel's algorithm?
Welch-Powell's algorithm is a graph coloring algorithm used to color the vertices of a graph such that no two adjacent vertices share the same color. It operates by sorting the vertices in descending order of their degrees and then assigning colors in a greedy manner, ensuring that each vertex receives the lowest available color that hasn't been assigned to its adjacent vertices. This approach is efficient for generating a proper vertex coloring, particularly for sparse graphs. The algorithm is notable for being simple to implement and often yields a near-optimal coloring.
What is the time complexity of the Kosaraju algorithm for finding strongly connected components in a directed graph?
The time complexity of the Kosaraju algorithm for finding strongly connected components in a directed graph is O(V E), where V is the number of vertices and E is the number of edges in the graph.
What is the runtime complexity of the Prim's algorithm for finding the minimum spanning tree of a graph?
The runtime complexity of Prim's algorithm is O(V2) or O(E log V), where V is the number of vertices and E is the number of edges in the graph.
What is the space complexity of breadth first search algorithm?
The space complexity of the breadth-first search algorithm is O(V), where V is the number of vertices in the graph being traversed.
What is the role of the vertex cover greedy algorithm in optimizing the selection of vertices to form a minimum vertex cover in a graph?
The vertex cover greedy algorithm helps in selecting the minimum number of vertices in a graph to cover all edges. It works by choosing vertices that cover the most uncovered edges at each step, leading to an efficient way to find a minimum vertex cover.
What is the algorithm used to find all pairs shortest paths in a graph efficiently?
The algorithm used to find all pairs shortest paths in a graph efficiently is called the Floyd-Warshall algorithm. It works by iteratively updating the shortest path distances between all pairs of vertices in the graph until the optimal solution is found.
