MTH 231 Lecture Notes - Lecture 11: If And Only If, Adjacency Matrix
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A tree is a connected undirected graph with no simple circuits. 1- a graph is a tree iff there is a unique simple path between any two distinct vertices. 2- a tree with vertices has exactly h-1 edges. A rooted there is a directed graph in which one vertex is designed as the root and all edges are directed away from the root. Si(cid:374)(cid:272)e edge dire(cid:272)tio(cid:374) (cid:272)a(cid:374) (cid:271)e i(cid:374)ferred fro(cid:373) the root, you do(cid:374)"t (cid:374)eed arrows root. This induced graph by ignoring the direction on the edges for a rooted there is a tree in the sense above. Identify vertex neighborhood n(v) & n(a) and division need: c(n, k) = (cid:4672)(cid:4673),(cid:4666),(cid:4667), Hand shake theorem (cid:2778) (cid:2779) (cid:2780) (cid:2781) (cid:882)(cid:882) (cid:883)(cid:882) (cid:882) (cid:883)(cid:883) (cid:882)]= (cid:2778)(cid:2779)(cid:2780)(cid:2781) [(cid:883) (cid:882) (cid:883) (cid:882) [(cid:882) (cid:883) (cid:882) (cid:882) (cid:882)(cid:882) (cid:883)(cid:882) (cid:882) (cid:883)(cid:883) (cid:882)][(cid:882) (cid:883) (cid:882) (cid:882) (cid:882) (cid:884) (cid:882) (cid:883) (cid:883) (cid:882) (cid:883) (cid:882) (cid:883) (cid:882) (cid:883) (cid:882) (cid:883)(cid:882) (cid:882)(cid:883) (cid:884) (cid:882)(cid:882) (cid:883)]
