On the Signless Laplacian Eigenvalues and Optimum SLE of Graph

Fuzzy Optimization and Modeling Journal

مقاله 5، دوره 3، شماره 2، تیر 2022، صفحه 40-45   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/fomj.2022.1950857.1059

نویسنده

Gholam Hossein Fath-Tabar^*

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran

چکیده

Let G be a graph of order n and with the vertex set {v_1,v_2,…,v_n } and the edge set E(G). The adjancency matrix of G is an n×n matrix A(G) whose (i,j)-entry is 1 if v_i is adjacent to v_j and 0, otherwise. Assume that D(G) is the n×n diagonal matrix whose (i,i)-entry is the degree of v_i. The matrices L(G) = D(G) - A(G) and Q(G) = D(G) + A(G) are called the Laplacian matrix and signless Laplacian matrix of G, respectively. The signelss Laplacian eigenvalues of a graph are the roots of characteristic polynomial of the signless Laplacian matrix of it. In this paper, we obtained signless Laplacian spectrum of some special subgraphs of complete graph and then estimated some bounds for signless Laplacian Energy of some graphs.

کلیدواژه‌ها

Signless Laplacian Spectrum؛ Signless Laplacian Energy؛ Signless Laplacian Eigenvalues؛ Graph