STRUKTUR GRAF DENGAN BARISAN DERAJAT {(m-1)^m,(n-1)^n } dan {m^n,n^m }

Abstract

A graph  consists of a set of vertices  and a set of edges . One of the essential aspects of a graph is the degree sequence, which represents the degrees of vertices and provides a concise summary of the graph’s characteristics. This study examines graphs with the degree sequence  where  vertices each have a degree of  and  vertices each have a degree of . This graph is degree-equivalent to the complete graph  but not isomorphic to it, denoted as . Meanwhile, the complement of this graph, denoted as , has the degree sequence , which is degree-equivalent to the bipartite graph  but is not isomorphic to it. In this paper, we prove the characteristics of these graphs, including connectivity, the existence of cut vertices and cut edges, as well as Hamiltonian properties, with  and pancyclic properties.

Keywords: Degree-equivalent, Degree sequence, Hamiltonian, Pancyclic