Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
474189 | Computers & Mathematics with Applications | 2008 | 7 Pages |
Abstract
Let GG be a graph on nn vertices, and let CHP(G;λ)CHP(G;λ) be the characteristic polynomial of its adjacency matrix A(G)A(G). All nn roots of CHP(G;λ)CHP(G;λ), denoted by λi(i=1,2,…n), are called to be its eigenvalues. The energy E(G)E(G) of a graph GG, is the sum of absolute values of all eigenvalues, namely, E(G)=∑i=1n|λi|. Let UnUn be the set of nn-vertex unicyclic graphs, the graphs with nn vertices and nn edges. A fully loaded unicyclic graph is a unicyclic graph taken from UnUn with the property that there exists no vertex with degree less than 3 in its unique cycle. Let Un1 be the set of fully loaded unicyclic graphs. In this article, the graphs in Un1 with minimal and second-minimal energies are uniquely determined, respectively.
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Dongdong Wang, Hongbo Hua,