cospectrality of two graphs measures the differences between the ordered spectrum of these graphs in various ways. actually,the origin of this concept came back to richard brualdi's problems that are proposed in cite{braldi}:let $g_n$ and $g'_n$ be two nonisomorphic simple graphs on $n$ vertices with spectra$$lambda_1 geq lambda_2 geq cdots geq lambda_n ;;;text{and};;; lambda'_1 geq lambda'_2 g...

We consider the problems of finding optimal identifying codes, (open) locating-dominating sets and resolving sets of an interval or a permutation graph. In these problems, one asks to find a subset of vertices, normally called a solution set, using which all vertices of the graph are distinguished. The identification can be done by considering the neighborhood within the solution set, or by emp...

This paper describes a probabilistic framework for graph-clustering. We commence from a set of pairwise distances between graph-structures. From this set of distances, we use a mixture model to characterize the pairwise affinity of the different graphs. We present an EM-like algorithm for clustering the graphs by iteratively updating the elements of the affinity matrix. In the M-step we applyin...

Given a social network, which of its nodes have a stronger impact in determining its structure? More formally: which node-removal order has the greatest impact on the network structure? We approach this well-known problem for the first time in a setting that combines both web graphs and social networks, using datasets that are orders of magnitude larger than those appearing in the previous lite...

in this paper, the degree distance and the gutman index of the corona product of two graphs are determined. using the results obtained, the exact degree distance and gutman index of certain classes of graphs are computed.

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...

in this paper, the weighted szeged indices of cartesian product and corona product of twoconnected graphs are obtained. using the results obtained here, the weighted szeged indices ofthe hypercube of dimension n, hamming graph, c4 nanotubes, nanotorus, grid, t− fold bristled,sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

Abstract. A divisor cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2,... | |} V such that an edge uv is assigned the label 1 if ( ) | ( ) f u f v or ( ) | ( ) f v f u and the label 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a divisor cordial labeling is called a divisor cordial graph. ...

See examples in Fig. 1(b). Many graph algorithms use an st-orientation. For instance, graph drawing algorithms [3], [4], [17], [19], [22], routing algorithms [1], [13] and partitioning algorithms [14]. Given a biconnected graph G and its two vertices s and t, one can find an st-orientation of G in O(m + n) time [5], [6], [22]. Note that if G is not biconnected then G may have no st-orientation....

A path graph is the intersection graph of subpaths of a tree. In 1970, Renz asked for a characterization of path graphs by forbidden induced subgraphs. We answer this question by determining the complete list of graphs that are not path graphs and are minimal with this property. 2009 Wiley Periodicals, Inc. J Graph Theory 62: 369–384, 2009