A simple undirected graph with all vertices having the same degree is called:a.Complete graphb.Bipartite graphc.Regular graphd.Eulerian graph

Explanation of the Concepts

1. Complete Graph: A complete graph is a graph where every pair of distinct vertices is connected by a unique edge. In a complete graph, every vertex has the same degree, which is equal to the total number of vertices minus one.

2. Bipartite Graph: A bipartite graph is a graph whose vertices can be divided into two disjoint sets such that no two graph vertices within the same set are adjacent. It does not necessarily imply that all vertices have the same degree.

3. Regular Graph: A regular graph is defined as a graph where each vertex has the same degree. This means that each vertex is connected to the same number of edges.

4. Eulerian Graph: An Eulerian graph is a graph in which there exists a closed trail that includes every edge exactly once. It relates more to the properties of edges rather than the uniformity of vertex degrees.

Final Answer

The correct option is c. Regular graph.