منابع مشابه
Graphs cospectral with starlike trees
A tree which has exactly one vertex of degree greater than two is said to be starlike. In spite of seemingly simple structure of these trees, not much is known about their spectral properties. In this paper, we introduce a generalization of the notion of cospectrality called m-cospectrality which turns out to be useful in constructing cospectral graphs. Based on this, we construct cospectral ma...
متن کاملCharacterization of 2-Path Product Signed Graphs with Its Properties
A signed graph is a simple graph where each edge receives a sign positive or negative. Such graphs are mainly used in social sciences where individuals represent vertices friendly relation between them as a positive edge and enmity as a negative edge. In signed graphs, we define these relationships (edges) as of friendship ("+" edge) or hostility ("-" edge). A 2-path product signed graph [Formu...
متن کاملEnumeration of cospectral graphs
We have enumerated all graphs on at most 11 vertices and determined their spectra with respect to various matrices, such as the adjacency matrix and the Laplacian matrix. We have also counted the numbers for which there is at least one other graph with the same spectrum (a cospectral mate). In addition we consider a construction for pairs of cospectral graphs due to Godsil and McKay, which we c...
متن کاملCospectral Graphs on 12 Vertices
We found the characteristic polynomials for all graphs on 12 vertices, and report statistics related to the number of cospectral graphs.
متن کاملNon-Isomorphic Graphs with Cospectral Symmetric Powers
The symmetric m-th power of a graph is the graph whose vertices are m-subsets of vertices and in which two m-subsets are adjacent if and only if their symmetric difference is an edge of the original graph. It was conjectured that there exists a fixed m such that any two graphs are isomorphic if and only if their m-th symmetric powers are cospectral. In this paper we show that given a positive i...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2018
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.04.021