Sharp spectral inequalities for connected bipartite graphs with maximal Q-index

Milica Anđelić, C. M. da Fonseca, Tamara Koledin, Zoran Stanić

Abstract


The Q-index of a simple graph is the largest eigenvalue of its signless Laplacian. As for the adjacency spectrum, we will show that in the set of connected bipartite graphs with fixed order and size, the bipartite graphs with maximal Q-index are the double nested graphs. We provide a sequence of (in)equalities regarding the principal eigenvector of the signless Laplacian of double nested graphs and apply these results to obtain some lower and upper bounds for their Q-index. In the end, we give some computational results in order to compare these bounds.

Keywords


Double nested graph, signless Laplacian, largest eigenvalue, spectral inequalities.

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DOI: https://doi.org/10.26493/1855-3974.271.85e

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications