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Minimality considerations for graph energy over a class of graphs

โœ Scribed by Dongdong Wang; Hongbo Hua

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
649 KB
Volume
56
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

Let G be a graph on n vertices, and let CHP(G; ฮป) be the characteristic polynomial of its adjacency matrix A(G). All n roots of CHP(G; ฮป), denoted by ฮป i (i = 1, 2, . . . n), are called to be its eigenvalues. The energy E(G) of a graph G, is the sum of absolute values of all eigenvalues, namely, E(G) = n i=1 |ฮป i |. Let U n be the set of n-vertex unicyclic graphs, the graphs with n vertices and n edges. A fully loaded unicyclic graph is a unicyclic graph taken from U n with the property that there exists no vertex with degree less than 3 in its unique cycle. Let U 1 n be the set of fully loaded unicyclic graphs. In this article, the graphs in U 1 n with minimal and second-minimal energies are uniquely determined, respectively.

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