The incidence energy I E (G) of a graph G, defined as the sum of the singular values of the incidence matrix of a graph G, is a much studied quantity with well known applications in chemical physics. The Laplacian-energy-like invariant of G is defined as the sum of square roots of the Laplacian eigenvalues. In this paper, we obtain the closed-form formulae expressing the incidence energy and th...

where n is the number of vertices of the graph G, and λ1,λ2, . . .,λn are its eigenvalues [1, 4, 5]. Two elementary properties of the graph energy are E(G1 ∪G2) = E(G1) + E(G2) for G1 ∪G2 being the graph consisting of two disconnected components G1 and G2, and E(G∪K1) = E(G), where K1 is the graph with a single vertex. Motivated by the success of the graph-energy concept, and in order to extend...

Let G be a connected graph of order n with Laplacian eigenvalues [Formula: see text]. The Laplacian-energy-like invariant of G, is defined as [Formula: see text]. In this paper, we investigate the asymptotic behavior of the 3.6.24 lattice in terms of Laplacian-energy-like invariant as m, n approach infinity. Additionally, we derive that [Formula: see text], [Formula: see text] and [Formula: see...

A b s t r a c t. Let G denote the complement of the graph G . If I(G) is some invariant of G , then relations (identities, bounds, and similar) pertaining to I(G) + I(G) are said to be of Nordhaus-Gaddum type. A number of lower and upper bounds of Nordhaus-Gaddum type are obtained for the energy and Laplacian energy of graphs. Also some new relations for the Laplacian graph energy are established.

In this paper simple formulae are derived for calculating the number of spanning trees of different product graphs. The products considered in here consists of Cartesian, strong Cartesian, direct, Lexicographic and double graph. For this purpose, the Laplacian matrices of these product graphs are used. Form some of these products simple formulae are derived and whenever direct formulation was n...

We consider performance analysis of interconnected linear dynamical networks subject to external stochastic disturbances. For stable linear networks, we define scalar performance measures by considering weighted H2–norms of the underlying systems, which are defined from the disturbance input to a desired output. It is shown that the performance measure of a general stable linear network can be ...