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arXiv · 1709.05473

Some improved bounds on two energy-like invariants of some derived graphs

Gui-Xian Tian·Shu-Yu Cui
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Abstract

Given a simple graph $G$, its Laplacian-energy-like invariant $LEL(G)$ and incidence energy $IE(G)$ are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. Applying the Cauchy-Schwarz inequality and the Ozeki inequality, along with its refined version, we obtain some improved bounds on $LEL$ and $IE$ of the $\mathcal {R}$-graph and $\mathcal{Q}$-graph for a regular graph. Theoretical analysis indicates that these results improve some known results. In addition, some new lower bounds on $LEL$ and $IE$ of the line graph of a semiregular graph are also given.

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Gui-Xian Tian, Shu-Yu Cui. 2017-09-16. Some improved bounds on two energy-like invariants of some derived graphs. https://arxiv.org/abs/1709.05473

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