The Signless Laplacian Estrada Index of Unicyclic Graphs
Hamid Reza Ellahi, Ramin Nasiri, Gholam Hossein Fath-Tabar, Ahmad, Gholami

TL;DR
This paper investigates the signless Laplacian Estrada index (SLEE) of unicyclic graphs, characterizing extremal graphs and identifying the maximum SLEE graph for given diameter.
Contribution
It characterizes unicyclic graphs with extremal SLEE values and determines the unique maximum SLEE unicyclic graph for fixed diameter.
Findings
Identified unicyclic graphs with the top two largest and smallest SLEE values.
Determined the unique unicyclic graph with maximum SLEE for a given number of vertices and diameter.
Abstract
For a graph , the signless Laplacian Estrada index is defined as ,where are the eigenvalues of the signless Laplacian matrix of . In this paper, we first characterize the unicyclic graphs with the first two largest and smallest and then determine the unique unicyclic graph with maximum among the unicyclic graphs on vertices with given diameter.
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Taxonomy
TopicsGraph theory and applications · Topological and Geometric Data Analysis · Synthesis and Properties of Aromatic Compounds
