A set S of vertices is an independent set if there are no edges between any two vertices in S (e.g., vertices of a common color form an independent set). An edge cover is a set C of vertices such that every edge is incident to a vertex in C. Show that in a graph H with vertex set V, if S is an edge cover, then V-S is an independent set. can you explain with examples or drawing?

Q: c) Let a graph have vertices G, H, I, J, K, L, M and edge set {{G, J}, {G, K}, {H, L}, {I, L}, {I,…

A:

Q: Construct a graph with vertices P, Q, R, S, T, U, V that has an Euler path, the degree of R is 1 and…

A:

Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: construct a graph with vertices Q,R,S,T,U,V,W that has an Euler path and the degree of U is 1 and…

A:

Q: by using python  TODO: add an undirected edge between node1 and node2

A: To add an undirected edge between node1 and node2 in Python, you need to first understand how to…

Q: Let a graph have vertices K, L, M, N, O, P, Q, R and edge set {{L, M}, {L, O}, {L, P), (L, R}, {M,…

A: Given that a graph have vertices  and following edge set..We need to find the degree of vertices .We…

Q: Construct a graph with vertices R, S, T, U, V that has an Euler circuit and the degree of T is 4.…

A:

Q: Construct a connected bipartite graph that is not a tree with vertices O, P, Q, R, S, T. What is the…

A:

Q: Suppose you colored edges of a graph either red or blue (not requiring that adjacent edges be…

A: According to the given information, Let the edges of the graph be coloured with red or blue. It is…

Q: Construct a bipartite graph with vertices A, B, C, D, E, F, G that is a tree. What is the edge set?…

A: Introduction: A unique type of graph known as a bipartite graph that exhibits the following…

Q: Construct a simple graph that is a forest with vertices B,C, D, E, F,G, H,I such that the degree of…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Shade the Venn Diagram to show the set. (AN D) UF' ..... A Use the graphing tool to shade the set.…

A:

Q: If v is an endpoint of a cut edge. Show that v is a cut vertex if and only if this vertex is not…

A: Let suppose that v is a cut vertex, i.e., that removing v and all of its incident edges increases…

Q: Use Euler's theorem to determine whether the graph has an Euler path (but not an Euler circuit),…

A: Given that, the graph has 102 even vertices and no odd vertices.

Q: 1) Construct a simple graph that is a forest with vertices M, N, O, P, Q, R such that the degree of…

A:

Q: Construct a simple graph with vertices F, G, H, I,J that has an Euler circuit and the degree of F is…

A: A graph is said to be simple if it has no loops and parallel edges. Degree of a vertex of a graph is…