In this paper, we provide an upper bound for the intersection number in join and corona of graphs. Moreover, give formulas Kn ◦G, Pn Cn ◦G Crn.

In this paper we determine when the join of two graphs is locally homogeneous. It is shown that the Cartesian product of a locally H1 graph and a locally H2 graph is locally (H1∪ H2). All graphs H of order at most 4 for which there are no locally H graphs are determined.

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.

Peg solitaire is a game generalized to connected graphs by Beeler and Hoilman. In the game pegs are placed on all but one vertex. If xyz form a 3-vertex path and x and y each have a peg but z does not, then we can remove the pegs at x and y and place a peg at z. By analogy with the moves in the original game, this is called a jump. The goal of the peg solitaire game on graphs is to find jumps t...

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