Question

explain why the two figures show equivalent graphs. then draw a third equivalent graph.
why are the two graphs equivalent? select all that apply.
a. the vertices are connected in the same way
b. the graphs have the same number of vertices.
c. the graphs have a number of edges that matches the number of vertices.
d. the graphs have the same number of edges
draw a third equivalent graph. choose the correct answer below.
a.
image of graph a
b.
image of graph b
c.
image of graph c
d.
image of graph d

Explanation:

• Option A: For two graphs to be equivalent (isomorphic), the vertices must be connected in the same way. If we label the vertices and check the adjacency (which vertices are connected by edges), if the connection - patterns match, this is a key property.
• Option B: The number of vertices is a necessary condition. If two graphs have a different number of vertices, they cannot be equivalent. Here, both graphs have 4 vertices.
• Option C: The number of edges matching the number of vertices is not a relevant condition for graph equivalence. For example, a graph with 4 vertices can have 3 edges (a tree) or 4 edges (a cycle plus an extra edge) and not be equivalent.
• Option D: The number of edges is a necessary condition. If two graphs have a different number of edges, they cannot be equivalent. Here, both graphs have 3 edges.

Answer:

A. The vertices are connected in the same way, B. The graphs have the same number of vertices, D. The graphs have the same number of edges.