Energy of Graphs

Please enable javascript in your browser.

Raoufi, Ensiyeh | 2020

445 Viewed

Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 53565 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari Feizabadi, Saeed; Fahmideh Gholami, Mahdi
Abstract:
Energy of graphs first defined by Ivan Gutman in 1978[1]. Let G be a graph with (0,1)-adjacency matrix A and let λ_1≥⋯≥λ_n be eigenvalues of A. Grap h energy is defined as the sum of absolute values of the eigenvalues of A and is shown by ɛ(G). let H_1,…,H_k be the vertex-disjoint induced subgraphs of graph G, it is proved that energy of G is at least equal to the sum of energy of H_i subgraphs, where the summation is over i. Also by partitioning edges of G to L_1,…,L_k subgraphs, energy of G is at most equal to sum of energy of L_i subgraphs , where the summation is over i. In this thesi s we study energy of graphs, specially graphs containing disjoint cycles and we present some upper and lower bounds on energy of graphs based on different parameters
Keywords:
Eigen Values ; Graph Energy ; Bound on Graph Energy ; Upper Bound Method ; Lower Bound

No TOC