A complete graph has a(n)______ between each pair of distinct vertices.
A)edge
B)path
C)cycle
D)circuit

Question

Quizplus · Accepted Answer

A complete graph has an edge between each pair of distinct vertices, hence the answer is A. A path is a sequence of edges connecting two distinct vertices, but in a complete graph, every vertex is connected to every other vertex, so there is no need for a path. A cycle is a closed path where all edges are distinct and all vertices except the first and last are distinct, but in a complete graph, there are no distinct vertices, so there cannot be a cycle. A circuit is a closed path that may contain repeated edges and vertices but does not repeat any other intermediate vertex, but again, in a complete graph, every vertex is adjacent to every other vertex, so there cannot be a circuit.

A Complete Graph Has A(n)______ Between Each Pair of Distinct