Original scientific paper

Tricyclic biregular graphs whose energy exceeds the number of vertices

Snježana Majstorović orcid.org/0000-0002-3083-0932 ; Department of Mathematics, University of Osijek,Osijek, Croatia
Ivan Gutman ; Faculty of Science, University of Kragujevac, Kragujevac, Serbia
Antoaneta Klobučar ; Department of Mathematics, University of Osijek,Osijek, Croatia

Abstract

The eigenvalues of a graph are the eigenvalues of its adjacency matrix. The energy $E(G)$ of the graph $G$ is the sum of the absolute values of the eigenvalues of $G$. A graph is said to be $(a,b)$-biregular if its vertex degrees assume exactly two different values: a and b. A connected graph with $n$ vertices and $m$ edges is tricyclic if m=n+2. The inequality $E(G)\geq n$ is studied for connected tricyclic biregular graphs, and conditions for its validity are established.

Keywords

energy (of a graph); biregular graph; tricyclic graph

Hrčak ID:

53226

URI

https://hrcak.srce.hr/53226

Publication date:

10.6.2010.

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