Energy of Graphs, Ph.D. Dissertation Sharif University of Technology ; Akbari, Saeid (Supervisor)
Abstract
Let G be a graph with adjacency matrix A and Δ be a diagonal matrix whose diagonal entries are the degree sequence of G. Then the matrices L = Δ− A and Q = Δ+A are called Laplacian matrix and signless Laplacian matrix of G, respectively. The eigenvalues of A, L, and Q are arranged decreasingly and denoted by λ1 ≥ · · · ≥ λn, μ1 ≥ · · · ≥ μn ≥ 0, and q1 ≥ · · · ≥ qn ≥ 0, respectively. The energy of a graph G is defined as E(G) :=
n i=1 |λi|. Furthermore, the incidence energy, the signed incidence energy, and the H¨uckel energy of G are defined as IE(G) := n i=1 √ qi, LE(G) := n i=1 √ μi, HE(G) := 2 r i=1 λi, n=... Cataloging briefEnergy of Graphs, Ph.D. Dissertation Sharif University of Technology ; Akbari, Saeid (Supervisor)
Abstract
Let G be a graph with adjacency matrix A and Δ be a diagonal matrix whose diagonal entries are the degree sequence of G. Then the matrices L = Δ− A and Q = Δ+A are called Laplacian matrix and signless Laplacian matrix of G, respectively. The eigenvalues of A, L, and Q are arranged decreasingly and denoted by λ1 ≥ · · · ≥ λn, μ1 ≥ · · · ≥ μn ≥ 0, and q1 ≥ · · · ≥ qn ≥ 0, respectively. The energy of a graph G is defined as E(G) :=
n i=1 |λi|. Furthermore, the incidence energy, the signed incidence energy, and the H¨uckel energy of G are defined as IE(G) := n i=1 √ qi, LE(G) := n i=1 √ μi, HE(G) := 2 r i=1 λi, n=... Find in contentBookmark |
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