A graph H is called a(n) ____ of G if V(H) is a subset of V(G) and E(H) is a subset of E(G); that is, every vertex of H is a vertex of G, and every edge in H is an edge in G.
A) matrix
B) intersection
C) subgraph
D) union

Question

Quizplus · Accepted Answer

The definition given describes a subgraph, where H is a smaller graph contained within the larger graph G, retaining only some of its vertices and edges. None of the other choices accurately describe this relationship. A matrix refers to a set of numbers arranged in rows and columns, and cannot be used to describe a graph. The intersection of two graphs would only refer to the set of vertices and edges shared by both, and would not necessarily include all vertices and edges in one graph as required by the definition. Finally, a union of graphs would create a larger graph that includes all vertices and edges from both graphs, and would not necessarily be a subset of either graph.

A Graph H Is Called A(n) ____ of G If