Abstract
In this paper, we consider a finite undirected and connected simple graph G(E, V) with vertex set V(G) and edge set E(G).We introduced a new computes the spectra of some operations on simple graphs [union of disjoint graphs, join of graphs, cartesian product of graphs, strong cartesian product of graphs, direct product of graphs].
Highlights
Graph theory and its applications has a long history, in structural mechanics and in particular nodal ordering and graph partitioning are well documented in the literature, Kaveh [11,12]
Algebraic graph theory can be considered as a branch of graph theory, where eigenvalues and eigenvectors of certain matrices are employed to deduce the principal properties of a graph
One of the major contributions in algebraic graph theory is due to Fiedler [9], where the properties of the second eigenvalue and eigenvector of the Laplacian of a graph have been introduced
Summary
Graph theory and its applications has a long history, in structural mechanics and in particular nodal ordering and graph partitioning are well documented in the literature, Kaveh [11,12]. The Laplacian matrix of a graph and its eigenvalues can be used in several areas of mathematical research and have a physical interpretation in various physical and chemical theories. The related matrix - the adjacency matrix of a graph and its eigenvalues were much more investigated in the past than the Laplacian matrix. The (ordinary) spectrum of a finite graph G is by definition the spectrum of theadjacency matrix A(G), that is, its set of eigenvalues together with their multiplicities.
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