Extremal unicyclic graphs  relative to the sum of the k-power degrees of the graphs

Ghalavand, َAli; Tavakoli, Mostafa

doi:10.22052/scj.2023.248230.1092

Extremal unicyclic graphs relative to the sum of the k-power degrees of the graphs

Articles in Press

Document Type : Original Article

Authors

َAli Ghalavand ¹
Mostafa Tavakoli ²

¹ Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, I. R. Iran

² Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P. O. Box 1159, Mashhad 91775, Iran

10.22052/scj.2023.248230.1092

Abstract

‎Let ‎G ‎be a ‎‎graph ‎and ‎d_G(v) ‎be ‎the ‎degree ‎of v ‎in ‎G‎. Then, the sum of the k-power degrees of ‎‎G ‎is ‎defined ‎as‎ ‎\Sigma_k(G) = \sum_{u \in V(G)}d_G(u)^k‎‎‎. ‎In this paper‎, ‎we obtain a relationship between Stirling number‎, ‎number of trees of subsets and the sum of the k-power degrees of the chemical graphs‎. ‎Also‎, ‎we characterize the extremal unicyclic graphs based on the sum of the k-power degrees of the graphs‎.

Keywords