In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex, and in a multigraph, loops are counted twice. The degree of a vertex <math>v</math> is denoted <math>\deg(v)</math> or <math>\deg v</math>. The maximum degree of a graph <math>G</math>, denoted by <math>\Delta(G)</math>, and the minimum degree of a graph, denoted by <math>\delta(G)</math>, are the maximum and minimum degree of its vertices. In the multigraph on the right, the maximum degree is 5 and the minimum degree is 0. | In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex, and in a multigraph, loops are counted twice. The degree of a vertex <math>v</math> is denoted <math>\deg(v)</math> or <math>\deg v</math>. The maximum degree of a graph <math>G</math>, denoted by <math>\Delta(G)</math>, and the minimum degree of a graph, denoted by <math>\delta(G)</math>, are the maximum and minimum degree of its vertices. In the multigraph on the right, the maximum degree is 5 and the minimum degree is 0. |