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Degree (Graph Theory)In the mathematical field of graph theory the degree or valency of a vertex v is the number of edges incident to v (with loops being counted twice). We write to denote the degree of v. In a directed graph the indegree of a vertex v is the number of edges terminating at v and the outdegree is the number of edges originating at v. We write and to denote the indegree and outdegree of v. A vertex with is called isolated. A vertex with is called a leaf. If each vertex of the graph has the same degree k the graph is called a k-regular graph and the graph itself is said to have degree k. A vertex with is called a source and a vertex with is called a sink. Some theorems Given a directed graph G for each vertex v of G -
The number of vertices with odd degree in any graph is even Given a graph G=(V,E) then -
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