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7.185  Articles
1 of 719 pages  |  10  records  |  more records»
Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. Generalizing the notion of gain graphs, skew gain graphs hav... 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

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

A graph G is said to be determined by its Laplacian spectrum (DLS) if every graph with the same Laplacian spectrum is isomorphic to G. A graph which is a collection of hexagons (lengths of these cycles can be different) all sharing precisely one vertex is... see more

For a finite commutative ring Zn with identity 1 ? 0, the zero divisor graph G(Zn) is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices x and y are adjacent if and only if xy=0. We... see more

The second smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity and denoted by a(G). We prove thata(G)>p2/3(p(12g(n1, n2, …, np)2 - p2)/4g(n1, n2, …, np)4 + 4(q - p)(3g(np + 1, np + 2, …, nq)2 - p... see more

Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and ano... 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

Suppose that Tnc is a set, such that the elements of Tnc are the complements of trees of order n. In 2012, Li and Wang gave the unique graph in the set Tnc \ {K1, n - 1c} with minimum 1st ‘least eigenvalue of the signless Laplacian’ (abbreviated to a LESL... see more

1 of 719 pages  |  10  records  |  more records»