Seidel energy of complete multipartite graphs

The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.

On the Seidel Energy of Certain Mesh Derived Networks

The energy of graph G is defined as the sum of the absolute values of eigenvalues of the adjacency matrix A(G). The manual calculation of energy of graphs consumes several man hours. In this paper, we use MATLAB to generate the Seidel matrix and hence calculate the Seidel energy of some mesh derived networks.

Seidel Equienergetic Graphs

The Seidel matrix S(G) of a graph G is the square matrix with diagonal entries zeroes and off diagonal entries are – 1 or 1 corresponding to the adjacency and non-adjacency. The Seidel energy SE(G) of G is defined as the sum of the absolute values of the eigenvalues of S(G). Two graphs G1 and G2 are said to be Seidel equienergetic if SE(G1) = SE(G2). We establish an expression for the characteristic polynomial of the Seidel matrix and for the Seidel energy of the join of regular graphs. Thereby construct Seidel non cospectral, Seidel equienergetic graphs on n vertices, for all n ≥ 12

QLS-integrality of complete r-partite graphs

A graph G is called A-integral (L-integral, Q-integral, S-integral) if the spectrum of its adjacency (Laplacian, signless Laplacian, Seidel) matrix consists entirely of integers. In this paper we study connections between the Q-(L,S,A) integral complete multipartite graphs. Moreover, new sufficient conditions for a construction of infinite families of QLS-integral complete r''-partite graphs Kp1,p2,...,pr'' = Kb1?p1,b2?p2,...,bs?ps from given QLS-integral r'-partite graphs Kp1,p2,...,pr' = Ka1?p1,a2?p2,...,as?ps are given. Using these conditions new infinite classes of such graphs for s = 4, 5, 6 are constructed, which affirmatively answers to questions proposed by Wang, Zhao and Li in [10, 14]. Finally, we propose open problems for further study.