The rigid all-versus-all adjacency required by a maximal biclique for its two vertex sets is extremely vulnerable to missing data. In the past, several types of quasi-bicliques have been proposed to tackle this problem, however their noise tolerance is usually unbalanced and can be very skewed. In this paper, we improve the noise tolerance of maximal quasi-bicliques by allowing every vertex to ...

a roman dominating function (rdf) on a graph g = (v,e) is defined to be a function satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. a set s v is a restrained dominating set if every vertex not in s is adjacent to a vertex in s and to a vertex in . we define a restrained roman dominating function on a graph g = (v,e) to be ...

The special combinatorial properties of graphic and co-graphic bondgraphs are analysed. A graphic bondgraph is one which has an associated graph, meaning that the two represent the same combinatorial information, expressed in thej’unctions of the bondgraph or the cycles of the graph. Dually a co-graphic bondgraph is one whose dual bondgraph has an associated graph. The combinatorial basis for c...

We study interrelations between symbolic descriptions of concurrently evolving systems and underlying sequential dynamics. We focus our interests on minimal shifts and t-shifts generated by them, assuming that an independence relation is given by a five vertex co-graph.

A graph G is well-covered if all its maximal independent sets are of the same cardinality. Assume that a weight function w is defined on its vertices. Then G is w-well-covered if all maximal independent sets are of the same weight. For every graph G, the set of weight functions w such that G is w-well-covered is a vector space, denoted WCW (G). Let B be a complete bipartite induced subgraph of ...

In many combinatorial situations there is a notion of independence of a set of points. Maximal independent sets can be easily constructed by a greedy algorithm, and it is of interest to determine, for example, if they all have the same size or the same parity. Both of these questions may be formulated by weighting the points with elements of an abelian group, and asking whether all maximal inde...

We consider the problem of inferring the opinions of a social network through strategically sampling a minimum subset of nodes by exploiting correlations in node opinions. We first introduce the concept of information dominating set (IDS). A subset of nodes in a given network is an IDS if knowing the opinions of nodes in this subset is sufficient to infer the opinion of the entire network. We f...

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.