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**public sources and our publisher partners.**A signed graph is a graph with a sign attached to each edge. This article extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the largest… Expand

In this note, a lower bound for the second largest eigenvalue of the Laplacian matrix of a graph is given in terms of the second largest degree of the graph.

A graphic sequence @p=(d"1,d"2,...,d"n) is said to be potentially K"r"+"1-graphic, if @p has a realization G containing K"r"+"1, a clique of r+1 vertices, as a subgraph. In this paper, we give two… Expand

Very little is known about upper bound for the largest eigenvalue of a tree with a given size of matching. In this paper, we find some upper bounds for the largest eigenvalue of a tree in terms of… Expand

Abstract In the note, we present an upper bound for the spectral radius of Laplacian matrix of a graph in terms of a “2-degree” of a vertex.

Abstract In this paper we determine the extremal graphs for which equality in de Caen's inequality holds and then apply the inequality to give an upper bound for the largest Laplacian eigenvalue λ 1… Expand

The normalized Laplacian of a graph was introduced by F.R.K. Chung and has been studied extensively over the last decade. In this paper, we introduce the notion of the normalized Laplacian of signed… Expand

Abstract A simple graph G is said to have property P k if it contains a complete subgraph of order k +1 as its subgraph. A nonincreasing sequence π of n nonnegative integers is potentially P k… Expand

Abstract A nonincreasing sequence π of n nonnegative integers is said to be graphic if it is the degree sequence of a simple graph G of order n and G is called a realization of π. A graph G of order… Expand

Abstract Gould et al. (Combinatorics, Graph Theory and Algorithms, Vol. 1, 1999, pp. 387–400) considered a variation of the classical Turan-type extremal problems as follows: For a given graph H ,… Expand