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3.737  Articles
1 of 375 pages  |  10  records  |  more records»
This paper is a survey on the upper and lower bounds for the largest eigenvalue of the Laplacian matrix, known as the Laplacian spectral radius, of a graph. The bounds are given as functions of graph parameters like the number of vertices, the number of e... see more

Let G be a simple undirected connected graph. In this paper, new upper bounds on the distance Laplacian spectral radius of G are obtained. Moreover, new lower and upper bounds for the distance signless Laplacian spectral radius of G are derived. Some of t... see more

The distance signless Laplacian spectral radius of a connected graph G is the largest eigenvalue of the distance signless Laplacian matrix of G?, ?defined as ?D?Q(G) = Tr(G) + D(G)?, ?where D(G) is the distance matrix of G and Tr(G) is the diagonal matrix... see more

?In this paper?, ?we study the eigenvalues of the reciprocal distance signless Laplacian matrix of a connected graph and??obtain some bounds for the maximum??eigenvalue of this matrix?. ?We also focus on bipartite graphs and find some bounds for the spect... see more

Let G be a simple connected graph with vertex set {1,2,...,n} and di denote the degree of vertex i in G. The ABC matrix of G, recently introduced by Estrada, is the square matrix whose ijth entry is v((di+dj-2)/didi); if i and j are adjacent, and zero; ot... see more

A bug Bugp,r1r2 is a graph obtained from a complete graph Kp by deleting an edge uv and attaching the paths Priand Pr2 by one of their end vertices at u and v, respectively. Let Q(G) be the signless Laplacian matrix of a graph G a... see more

Both the enhancement of the aerosol number concentration and the relative dispersion of the cloud droplet size distribution (spectral dispersion) on a regional scale can modify the cloud reflectivity. This work is focused on the ... see more

Rigidity is the property of a structure that does not flex under an applied force. In the past several decades, the rigidity of graphs has been widely studied in discrete geometry and combinatorics. Laman (1970) obtained a combinatorial characterization o... see more

In this paper, we determine the graphs (respectively, trees) with maximum spectral radius among all graphs (respectively, trees) with zero forcing number at most kk.  As an application, we give a sharp lower bound for the zero forcing number of graph... see more

1 of 375 pages  |  10  records  |  more records»