vertex-degree

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

Which of the following statements is/are TRUE for undirected graphs? P: Number of odd degree vertices is even. Q: Sum of degrees of all vertices is even.

$$G$$ is a simple undirected graph. Some vertices of $$G$$ are of odd degree. Add a node $$v$$ to $$G$$ and make it adjacent to each odd degree vertex of $$G$$. The resultant graph...