Matching Energy of Unicyclic and Bicyclic Graphs with a Given Diameter

Lin Chen; Jinfeng Liu; Yongtang Shi

Matching Energy of Unicyclic and Bicyclic Graphs with a Given Diameter

Combinatorics 2014-09-09 v1

Authors: Lin Chen , Jinfeng Liu , Yongtang Shi

Abstract

Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $\mu_1,\mu_2,\ldots,\mu_n$ be the roots of its matching polynomial. The matching energy of $G$ is defined to be the sum of the absolute values of $\mu_{i}\ (i=1,2,\ldots,n)$ . In this paper, we characterize the graphs with minimal matching energy among all unicyclic and bicyclic graphs with a given diameter $d$ .

Keywords

matching energy unicyclic graphs bicyclic graphs graph diameter matching polynomial minimal energy

Cite

@article{arxiv.1409.2039,
  title  = {Matching Energy of Unicyclic and Bicyclic Graphs with a Given Diameter},
  author = {Lin Chen and Jinfeng Liu and Yongtang Shi},
  journal= {arXiv preprint arXiv:1409.2039},
  year   = {2014}
}

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28 pages, 9 figures, accepted for publication, Complexity, 2014

Matching Energy of Unicyclic and Bicyclic Graphs with a Given Diameter

Abstract

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