Open AccessPosted Content
Eigenvalues of a H-generalized join graph operation constrained by vertex subsets
Reads0
Chats0
TLDR
In this article, a generalized H-generalized join operation of a family of graphs constrained by a set of vertex subsets is introduced, and lower and upper bounds on the spread of non-regular graphs of order n are derived.Abstract:
Considering a graph $H$ of order $p$, a generalized $H$-join operation of a family of graphs $G_1,..., G_p$, constrained by a family of vertex subsets $S_i \subseteq V(G_i)$, $i=1,..., p,$ is introduced. When each vertex subset $S_i$ is $(k_i,\tau_i)$-regular, it is deduced that all non-main adjacency eigenvalues of $G_i$, different from $k_i-\tau_i$, for $i=1,..., p,$ remain as eigenvalues of the graph $G$ obtained by the above mentioned operation. Furthermore, if each graph $G_i$ of the family is $k_i$-regular, for $i=1,..., p$, and all the vertex subsets are such that $S_i=V(G_i)$, the $H$-generalized join operation constrained by these vertex subsets coincides with the $H$-generalized join operation. Some applications on the spread of graphs are presented. Namely, new lower and upper bounds are deduced and a infinity family of non regular graphs of order $n$ with spread equals $n$ is introduced.read more
Citations
More filters
Journal ArticleDOI
Spectra of Graphs Resulting from Various Graph Operations and Products: a Survey
TL;DR: In this paper, a survey of known results about the spectra of the adjacency, Laplacian and signless L 1 matrix of graphs resulting from various graph operations is presented.
Posted Content
Joins of Hypergraphs and Their Spectra
Amitesh Sarkar,Anirban Banerjee +1 more
TL;DR: The definition of equitable partition and joining operation for hypergraphs is extended, and those to compute eigenvalues of differenthypergraphs are used to derive the characteristics polynomial of a complete-uniform hypergraph and how to generate infinitely many pairs of non-isomorphic co-spectral hyper graphs.
Posted Content
Spectra of $(H_1,H_2)$-merged subdivision graph of a graph.
R. Rajkumar,M. Gayathri +1 more
TL;DR: A ternary graph operation is defined which generalizes the construction of subdivision graph, R-$graph, central graph, and consequently, Q-graph, totalgraph, and quasitotal graph and derives the L-spectrum of the graphs obtained by the unary graph operations.
Journal ArticleDOI
Ky Fan theorem applied to Randić energy
TL;DR: In this paper, Fan established an inequality between the sum of singular values of X, Y, and Z, and applied this inequality to obtain bounds on the Randic energy of a symmetric partitioned matrix, as well as an application to the coalescence of graphs.
Journal ArticleDOI
Spectra of M-edge rooted product of graphs
R. Pavithra,R. Rajkumar +1 more
TL;DR: In this article, a graph operation called M-edge rooted product of graphs is defined and a matrix invariant is introduced, namely, coronal of a matrix constrained by the index sets.
References
More filters
Book
Topics in Matrix Analysis
TL;DR: The field of values as discussed by the authors is a generalization of the field of value of matrices and functions, and it includes singular value inequalities, matrix equations and Kronecker products, and Hadamard products.
Book ChapterDOI
Computing the characteristic polynomial of a graph.
TL;DR: In this paper, the eigenvalues of a graph are computed by searching for p orthogonal eigenvectors, determining the first p moments by counting closed walks and then finding the spectrum from the moments, or using certain subgraphs to determine the coefficients of the characteristic polynomial.
Journal ArticleDOI
The spread of a matrix
TL;DR: The problem of estimating the maximum distance between two characteristic roots of a given matrix does not appear to have attracted much attention as discussed by the authors, although there is an extensive literature dealing with the location of characteristic roots.
Journal ArticleDOI
Spectra of graphs obtained by a generalization of the join graph operation
TL;DR: A more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs.
Journal ArticleDOI
The spread of the spectrum of a graph
TL;DR: In this paper, upper and lower bounds for the spread of the adjacency matrix of a simple graph were obtained for the eigenvalues λ 1 λ 2 ··· λn.