Short note on Randi\'{c} energy

Luiz Emilio Allem; Gonzalo Molina; Adrián Pastine

Short note on Randi\'{c} energy

Combinatorics 2018-11-22 v1

Authors: Luiz Emilio Allem , Gonzalo Molina , Adrián Pastine

Abstract

In this paper, we consider the Randi\'{c} energy $RE$ of simple connected graphs. We provide upper bounds for $RE$ in terms of the number of vertices and the nullity of the graph. We present families of graphs that satisfy the Conjecture proposed by Gutman, Furtula and Bozkurt \cite{Gutman1} about the maximal RE. For example, we show that starlikes of odd order satisfy the conjecture.

Keywords

graph energy

Cite

@article{arxiv.1811.08776,
  title  = {Short note on Randi\'{c} energy},
  author = {Luiz Emilio Allem and Gonzalo Molina and Adrián Pastine},
  journal= {arXiv preprint arXiv:1811.08776},
  year   = {2018}
}

Comments

14 pages

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