scholarly journals Tricyclic graph with maximal Estrada index

2014 ◽  
Vol 162 ◽  
pp. 364-372 ◽  
Author(s):  
Zhongxun Zhu ◽  
Liansheng Tan ◽  
Zhongyi Qiu
Keyword(s):  
Estrada Index ◽  
Tricyclic Graph

scholarly journals A Note on the Estrada Index of the Aα-Matrix

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 811
Author(s):  
Jonnathan Rodríguez ◽  
Hans Nina
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Estrada Index

Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A(G) and D(G) and defined the Aα-matrix for every real α∈[0,1] as: Aα(G)=αD(G)+(1−α)A(G). In this paper, using a different demonstration technique, we present a way to compare the Estrada index of the Aα-matrix with the Estrada index of the adjacency matrix of the graph G. Furthermore, lower bounds for the Estrada index are established.

scholarly journals The Tight Upper Bound for the Number of Matchings of Tricyclic Graphs

10.37236/2165 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Ardeshir Dolati ◽  
Somayyeh Golalizadeh
Keyword(s):  
Upper Bound ◽  
Fibonacci Number ◽  
Tricyclic Graph ◽  
Tricyclic Graphs

In this paper, we determine the tight upper bound for the number of matchings of connected $n$-vertex tricyclic graphs. We show that this bound is $13 f_{n-4} + 16f_{n-5}$, where $f_n$ be the  $n$th Fibonacci number. We also  characterize the $n$-vertex simple connected tricyclic graph for which the bound is best  possible.A corrigendum was added to this paper on Jun 17, 2015. 

scholarly journals The Estrada index of unicyclic graphs

2012 ◽  
Vol 436 (9) ◽  
pp. 3149-3159 ◽  
Author(s):  
Zhibin Du ◽  
Bo Zhou
Keyword(s):  
Unicyclic Graphs ◽  
Estrada Index

New Bounds for the Estrada Index of Phenylenes

2020 ◽  
pp. 1-17
Author(s):  
Muhammad Aamer Rashid ◽  
Sarfraz Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
Akbar Jahanbani ◽  
S. M. Sheikholeslami ◽  
...  
Keyword(s):  
Estrada Index

Hermitian energy and Hermitian Estrada index of digraphs

2019 ◽  
Vol 13 (06) ◽  
pp. 2050116 ◽  
Author(s):  
Akbar Jahanbani
Keyword(s):  
Lower Bounds ◽  
Adjacency Matrix ◽  
Hermitian Matrix ◽  
Upper And Lower Bounds ◽  
Estrada Index

Let [Formula: see text] be a digraph of order [Formula: see text], and [Formula: see text] be spectrum of the Hermitian adjacency matrix. The main purpose of this paper is to introduce the Hermitian energy and Hermitian Estrada index of a digraph, both based on the eigenvalues of the Hermitian matrix. Moreover, we establish upper and lower bounds for these new digraph invariants, and relations between them.

scholarly journals Estimating the Estrada index

2007 ◽  
Vol 427 (1) ◽  
pp. 70-76 ◽  
Author(s):  
José Antonio de la Peña ◽  
Ivan Gutman ◽  
Juan Rada
Keyword(s):  
Estrada Index

scholarly journals The Laplacian energy and Laplacian Estrada index of random multipartite graphs

2016 ◽  
Vol 443 (2) ◽  
pp. 675-687 ◽  
Author(s):  
Dan Hu ◽  
Xueliang Li ◽  
Xiaogang Liu ◽  
Shenggui Zhang
Keyword(s):  
Estrada Index ◽  
Laplacian Energy ◽  
Multipartite Graphs
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