We define the Cartesian product, composition, union and join on interval-valued fuzzy graphs and investigate some of their properties. We also introduce the notion of interval-valued fuzzy complete graphs and present some properties of self complementary and self weak complementary interval-valued fuzzy complete graphs.

We introduce H -join decompositions of graphs, indexed by a fixed bipartite graph H . These decompositions are based on a graph operation that we call H -join, which adds edges between two given graphs by taking partitions of their two vertex sets, identifying the classes of the partitions with vertices of H , and connecting classes by the pattern H . H -join decompositions are related to modul...

In this contribution, we first investigate sharp bounds for the reciprocal sum-degree distance of graphs with a given matching number. The corresponding extremal graphs are characterized completely. Then we explore the k-decomposition for the reciprocal sum-degree distance. Finally,we establish formulas for the reciprocal sum-degree distance of join and the Cartesian product of graphs.

In this paper we study the behavior of the second edge-Wiener index under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs. 2010 Mathematics Subject Classification: 05C12; 05C62; 92E10

We prove that perfect graphs with no balanced skew-partitions admits a O(n) Clique-Stable set separator. We then prove that for every graph G in this class, there always exists two subsets of vertices V1, V2 such that |V1|, |V2| ≥ c|V (G)| for some constant c and V1 is either complete or anticomplete to V2. The method uses trigraphs, introduced by Chudnovsky [5], and relies on the good behavior...

In many applications, the underlying data (the web, an XML document, or a relational database) can be seen as a graph. These graphs may be enriched with weights, associated with the nodes and edges of the graph, denoting application specific desirability/penalty assessments, such as popularity, trust, or cost. A particular challenge when considering such weights in query processing is that resu...

In this paper, we study the connectivity of the complement of a graph. We first establish a simple formula to compute the connectivity of a graph that comes from the join of graphs. Base on this formula, we give an upper and a lower bound to the connectivity of the complement of a graph. Keyword: connectivity, complement, join, vertex of attachment.

This paper is a contribution to the study of a quasi-order on the set Ω of Boolean functions, the simple minor quasi-order. We look at the join-irreducible members of the resulting poset˜Ω. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield...