The adjacency matrix of a signed graph has -1 or +1 for adjacent vertices, depending on the sign of the connecting edges. In this paper, the eigenvalues of signed complete graphs are investigated. We prove that -1 and 1 are the eigenvalues of the signed complete graph with the ...
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 Laplacian eigenvalue of a signed graph is investigated, which generalizes the corresponding results on the...
On the eigenvalues of A α -matrix of graphs 来自 Semantic Scholar 喜欢 0 阅读量: 141 作者:S Liu,KC Das,J Shu 摘要: Let G be a graph with adjacency matrix A(G) and let D(G) be the diagonal matrix of the degrees of G. For every real α∈[0,1], Nikiforov defined the matrix...
On the extreme eigenvalues of regular graphs - Cioabǎ - 2005 () Citation Context ...3 nm (n 2 − 2m) with equality if and only if G is a regular complete multipartite graph. (5) From Theorem 3 we effortlessly deduce results complementary to results of Serre, Li, and Cioabă (...
of graphs have a close relationship to strongly regular graphs.In this paper, we study the distance eigenvalues of the design graphs.Also, we will explicitly determine the distance eigenvalues of a class ofdesign graphs, and determine the values for which the class is distanceintegral, that is,...
We consider undirected non-regular connected graphs without loops and multiple edges (other than complete bipartite graphs) which have exactly three distinct eigenvalues (such graphs are called non-standard graphs). The interest in these graphs is motivated by the questions posed by W. Haemers durin...
graph theory/ eigenvalueseigenvectorsbipartite graphs/ C1160 Combinatorial mathematicsThe established, spectral characterisation of bipartite graphs with unweighted vertices (which are here termed homogeneous graphs) is extended to those bipartite graphs (called heterogeneous) in which all of the vertices in ...
In this article we examine the adjacency and Laplacian matrices and their eigenvalues and energies of the general product (non-complete extended p-sum, or NEPS) of signed graphs. We express the adjacency matrix of the product in terms of the Kronecker matrix product and the eigenvalues and ener...
We characterize all connected graphs with exactly three distinct normalized Laplacian eigenvalues among which one is equal to 1, and determine all connected bipartite graphs with at least one vertex of degree 1 having exactly four distinct normalized Laplacian eigenvalues. In addition, we find all uni...
Eigenvalues and chromatic number of a signed graph For a signed graph Sigma, let chi(Sigma), lambda(1) and lambda(n) be the chromatic number, the maximum eigenvalue and the minimum eigenvalue of Sigma, resp... ZQJ Wang - 《Linear Algebra & Its Applications》 被引量: 0发表: 2021年 加...