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This document contains solutions to 6 exercises on graph theory from Lecture 1. 1) It proves that the number of vertices of odd degree in any graph is even using the Handshaking Lemma. 2) It shows that an r-regular graph with n vertices has nr/2 edges. 3) It finds that the number of edges in a complete graph Kn is n(n-1)/2. 4) It finds that the number of edges in a complete bipartite graph Kn,n is n2. 5) It proves that there is no graph with the given conditions of 12 vertices, 28 edges, and degrees of 3

Author

mirzag1782

Language

EN