Mulas, Raffaella Stanić, Zoran
Published in
Special Matrices

In this article, we investigate connected signed graphs which have a connected star complement for both −2-2 and 2 (i.e. simultaneously for the two eigenvalues), where −2-2 (resp. 2) is the least (largest) eigenvalue of the adjacency matrix of a signed graph under consideration. We determine all such star complements and their maximal extensions (a...

Bensmail, Julien Inerney, Fionn Mc Lyngsie, Kasper Szabo
Published in
Discussiones Mathematicae Graph Theory

For any S ⊂ ℤ we say that a graph G has the S-property if there exists an S-edge-weighting w : E(G) → S such that for any pair of adjacent vertices u, v we have ∑e∈E(v) w(e) ≠ ∑e∈E(u) w(e), where E(v) and E(u) are the sets of edges incident to v and u, respectively. This work focuses on {a, a + 2}-edge-weightings where a ∈ ℤ is odd. We show that a ...

Pirzada, S. Barati, Z. Afkhami, M.
Published in
Acta Universitatis Sapientiae, Informatica

Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×. In this paper, we determine the Laplacian and signless Laplacian e...

Prashanth, B. Naik, K. Nagendra M, R. Salestina
Published in
Journal of Applied Mathematics, Statistics and Informatics

With this article in mind, we have found some results using eigenvalues of graph with sign. It is intriguing to note that these results help us to find the determinant of Normalized Laplacian matrix of signed graph and their coe cients of characteristic polynomial using the number of vertices. Also we found bounds for the lowest value of eigenvalue...

He, Changxiang Li, Yuying Shan, Haiying Wang, Wenyan
Published in
Computational and Applied Mathematics

In this paper, we focus on the index (largest eigenvalue) of the adjacency matrix of connected signed graphs. We give some general results on the index when the corresponding signed graph is perturbed. As applications, we determine the first five largest indices among all unbalanced signed bicyclic graphs on n≥36\documentclass[12pt]{minimal} \usepa...

Zhang, Peikang Wu, Baofeng He, Changxiang
Published in
Computational and Applied Mathematics

In this paper, we consider a generalized join operation, the H˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot{H}$$\end{document}-join on signed graphs, where H˙\d...

Stanić, Zoran
Published in
Special Matrices

We derive an inequality that includes the largest eigenvalue of the adjacency matrix and walks of an arbitrary length of a signed graph. We also consider certain particular cases.

Estrada, Ernesto

The Estrada index of a graph/network is defined as the trace of the adjacency matrix exponential. It has been extended to other graph-theoretic matrices, such as the Laplacian, distance, Seidel adjacency, Harary, etc. Here, we describe many of these extensions, including new ones, such as Gaussian and Mittag-Leffler ones. More importantly, we conte...

Mathias, Anisha Jean Sangeetha, V. Acharya, Mukti
Published in
Acta Universitatis Sapientiae, Mathematica

A signed graph Σ is a graph with positive or negative signs attatched to each of its edges. A signed graph Σ is balanced if each of its cycles has an even number of negative edges. Restrained dominating set D in Σ is a restrained dominating set of its underlying graph where the subgraph induced by the edges across Σ[D : V \ D] and within V \ D is b...

Du, Zhibin da Fonseca, Carlos M. Losonczi, László
Published in
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

In this note, we generalize an interesting recent characterization of tridiagonal M-matrices whose inverse is still tridiagonal to any acyclic matrix. We discuss a possible extension. Several illustrative examples are provided.