Vipul: Created page with "{{undirected graph vertex numerical invariant}} ==Definition== ===Definition for an undirected graph without loops, parallel edges, or weights=== Suppose $G$ is ..."

2012-05-28T17:16:45Z

Created page with "{{undirected graph vertex numerical invariant}} ==Definition== ===Definition for an undirected graph without loops, parallel edges, or weights=== Suppose <math>G</math> is ..."

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{{undirected graph vertex numerical invariant}}

==Definition==

===Definition for an undirected graph without loops, parallel edges, or weights===

Suppose <math>G</math> is an [[undirected graph]] and <math>x</math> is a vertex of <math>G</math>. The '''degree''' or '''valency''' of <math>x</math> is defined as the number of vertices of <math>G</math> adjacent to <math>x</math>, or equivalently, as the number of edges of <math>G</math> that have <math>x</math> as one of their endpoints. Explicitly, if <math>V(G)</math> and <math>E(G)</math> denote the vertex set and edge set, the degree of <math>x</math> is:

<math>| \{ y \in V(G) \mid \{ x, y \} \in E(G) \}|</math>

Degree of a vertex - Revision history

Vipul: Created page with "{{undirected graph vertex numerical invariant}} ==Definition== ===Definition for an undirected graph without loops, parallel edges, or weights=== Suppose G is ..."

Vipul: Created page with "{{undirected graph vertex numerical invariant}} ==Definition== ===Definition for an undirected graph without loops, parallel edges, or weights=== Suppose $G$ is ..."