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

Astri Widyawati Sulistyo Cahyani
I Ketut Budayasa

MATHunesa: Jurnal Ilmiah Matematika
Vol. 13 No. 2 (2025)

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