the stability of a communication network composed of processing nodes and communication links is of prime importance to network designers. as the network begins losing links or nodes, eventually there is a loss in its effectiveness. thus, communication networks must be constructed to be as stable as possible, not only with respect to the initial disruption, but also with respect to the possible...

The eigenvalues of a graph is the root of its characteristic polynomial. A fullerene F is a 3- connected graphs with entirely 12 pentagonal faces and n/2 -10 hexagonal faces, where n is the number of vertices of F. In this paper we investigate the eigenvalues of a class of fullerene graphs.

The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.

A clustered graph C = (G; T ) consists of an undirected graph G and a rooted tree T in which the leaves of T correspond to the vertices of G = (V;E). Each vertex c in T corresponds to a subset of the vertices of the graph called \cluster". c-planarity is a natural extension of graph planarity for clustered graphs, and plays an important role in automatic graph drawing. The complexity status of ...

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

A graph of order n is p-factor-critical, where p is an integer of the same parity as n, if the removal of any set of p vertices results in a graph with a perfect matching. 1-factor-critical graphs and 2-factor-critical graphs are well-known factor-critical graphs and bicritical graphs, respectively. It is known that if a connected vertextransitive graph has odd order, then it is factor-critical...

By applying the Tutte decomposition of 2{connected graphs into 3{block trees we provide unique structural characterizations of several classes of 2{connected graphs, including minimally 2{connected graphs, minimally 2{edge{connected graphs, critically 2{connected graphs, critically 2{edge{connected graphs, 3{edge{connected graphs, 2{connected cubic graphs and 3{connected cubic graphs. We also g...