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This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]

Spectra of weighted networks have received increasing attention from scientific community, such as mathematical chemistry, computer science, coding theory. The real networks behavior is completely differently, not only in the degree distribution, but also in the weight distribution. In this paper, we determine the generalized adjacency (resp., Laplacian and signless Laplacian) spectra of the weighted neighbourhood corona networks with different structures. As applications, the two important indices of the weighted neighbourhood corona networks are computed. [ABSTRACT FROM AUTHOR]

A vertex u ∈ V1 in a bipartite graph G(V1∪V2;E) is redundant if all the vertices of V2 that are adjacent to u are also adjacent to a vertex w (≠= u) in V1. In other words, NG(u) ⊆ NG(w). Such vertices increase the cost of the network (when it is a communication network) or increase the unnecessary membership of the network (when it is a social network). An ideal cost effective network is the one where there is no redundant vertex. In this article, we model the above type of networks using graphs and call them antichain graphs. We characterize such graphs and study their properties. We show that if G and H are antichain graphs then so is their cartesian product G x H. We design few more methods to construct new antichain graphs from the existing ones. We also present generating procedures, which generate some regular and biregular antichain graphs. We define a critical edge with reference to the antichain property. We also characterize the critical edge. [ABSTRACT FROM AUTHOR]

For a graph G, let A(G) and D(G) be the adjacency matrix and the degree matrix of G, respectively. Nikiforov defined the matrix Aα(G) as where α ∊ [0; 1]. In this paper, we first give the Aα-spectral radius of semistrong product of arbitrary graph G and a regular graph H. Then we respectively present the Aα-spectra of semistrong product G•H and special product G⊕H when G and H are two regular graphs. Moreover, we give the Aα-spectral radius of wreath product GρH. [ABSTRACT FROM AUTHOR]

The energy of G is defined as the sum of absolute value of all eigenvalues of the adjacency matrix A(G). Let B²(n, a, b, p) be the set of all bicyclic graphs on n vertices with p pendent vertices and two cycles Ca and Cb which have unique common vertex u0, Bθ²(n, a, b, p) the graph class obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sn-(a + b - 1)+1, and Bµ² (n, a, b, p) the set obtained by coinciding the common vertex u0 of Ca and Cb with the center of the star Sp and connecting a pendent path Pn - (a + b -1)-(p - 1) on point u0. In this paper, it is obtained that Bθ² (n, a, b, p) has the minimal energy in all graphs which have only pendent vertices except two cycles, and Bµ² (n, a, b, p) has the minimal energy in all graphs which have prescribed cycles' length and pendent vertices. [ABSTRACT FROM AUTHOR]