Proof. Let ( G = (V, E) ) be a graph. By the Handshaking Lemma, ( \sum_v \in V \deg(v) = 2|E| ), which is even. The sum of even degrees is even. Therefore, the sum of odd degrees must also be even. The sum of an odd number of odd integers is odd; thus, the number of vertices with odd degree must be even. ∎
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By combining the solution manual with these additional resources, you can develop a deeper understanding of graph theory and its applications. Proof. Let ( G = (V
: Many exercises are designed to introduce readers to open research questions or historical conjectures. Hints for Starred Problems Solution Manual Of Graph Theory By Bondy And Murty