If for some positive integer k, degree of vertex d(v) = k for every vertex v of the graph G, then G is called -
If for some positive integer k, degree of vertex d (v) = k for every vertex v of the graph G, then G is called K-regular graph.
Graph theoryis the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices, nodes, or points which are connected by edges, arcs, or lines.
A regular graph is a graph where each vertex has the same number of neighbors; that is every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other.
The degree of a vertex of a graph is the number of edges incident to the vertex, with loops counted twice. In the graph on the right, the maximum degree is 5 and the minimum degree is 0.