Consider an undirected graph G that has n distinct vertices. Assume n≥3. How many distinct edges...

Consider an undirected graph G that has n distinct vertices. Assume n≥3.

How many distinct edges will there be in any circuit for G that contains all the vertices in G?
What is the maximum degree that any vertex in G can have?
What is the maximum number of distinct edges G can have?
What is the maximum number of distinct edges that G can have if G is disconnected?

Expert Solution

ekkarill92 answered 2 years ago

Given an undirected graph G = (V,E), consisting of n vertices and m edges, with each...

Given an undirected graph G = (V,E), consisting of n vertices and m edges, with each edge labeled from the set {0,1}. Describe and analyze the worst-case time complexity of an efficient algorithm to find any cycle consisting of edges whose labels alternate 0,1.

Null graph,Nn, n=1,2,3,4...，the graph with n vertices and no edges. (N4=4 vertices with no edges) 4...

Null graph,Nn, n=1,2,3,4...，the graph with n vertices and no edges. (N4=4 vertices with no edges) 4 a) find a graph with 8 vertices with no 3-cycles and no induced sub graph isomorphic to N4 b)prove that every simple graph with 9 vertices with no 3-cycles has an induced sub graph isomorphic to N4

Let G be a simple undirected graph with n vertices where n is an even number....

Let G be a simple undirected graph with n vertices where n is an even number. Prove that G contains a triangle if it has at least (n^2 / 4) + 1 edges using mathematical induction.

If graph G has n edges and k component and m vertices, so m ≥ n-k....

If graph G has n edges and k component and m vertices, so m ≥ n-k. Prove it!

If graph g has n vertices and k component and m edges, so m ≥ n-k....

If graph g has n vertices and k component and m edges, so m ≥ n-k. Prove it ! Thank you...

Write a complete Java program which takes vertices and edges of an undirected graph from the...

Write a complete Java program which takes vertices and edges of an undirected graph from the input file input.txt (the graph as adjacency matrix) ,(adjacent vertics of every vertex ),(DFS traversal of the graph),(BFS traversal of the graph),(Graph is connected or not connected)

You are given a directed graph G(V,E) with n vertices and m edges. Let S be...

You are given a directed graph G(V,E) with n vertices and m edges. Let S be the subset of vertices in G that are able to reach some cycle in G. Design an O(n + m) time algorithm to compute the set S. You can assume that G is given to you in the adjacency-list representation.

5. Suppose we are given both an undirected graph G with weighted edges and a minimum...

5. Suppose we are given both an undirected graph G with weighted edges and a minimum spanning tree T of G . (a) Describe an algorithm to update the minimum spanning tree when the weight of a single edge e is decreased. (b) Describe an algorithm to update the minimum spanning tree when the weight of a single edge e is increased. In both cases, the input to your algorithm is the edge e and its new weight; your algorithms...

Prove a connected simple graph G with 16 vertices and 117 edges is not Eulerian.

A graph is G is semi-Eulerian if there are distinct vertices u, v ∈ V (G),...

A graph is G is semi-Eulerian if there are distinct vertices u, v ∈ V (G), u =v such that there is a trail from u to v which goes over every edge of G. The following sequence of questions is towards a proof of the following: Theorem 1. A connected graph G is semi-Eulerian (but not Eulerian) if and only if it has exactly two vertices of odd degree. Let G be semi-Eulerian with a trail t starting at...

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