The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There was collected the exact values of crossing numbers for join of all graphs of at most four vertices and of several graphs of order five with paths and cycles. We extend these r...

Graph theory has an important role in the area of applications of networks and clustering‎. ‎In the case of dealing with uncertain data‎, ‎we must utilize ambiguous data such as fuzzy value‎, ‎fuzzy interval value or values of fuzzy number‎. ‎In this study‎, ‎values of fuzzy number were used‎. ‎Initially‎, ‎we utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value f...

i.p.s. hypergroups are canonical hypergroups such that$[forall(a,x),a+xni x]Longrightarrow[a+x=x].$i.p.s. hypergroups were investigated in [1], [2], [3], [4] and it was proved thatif the order is less than 9, they are strongly canonical (see [13]). In this paperwe obtain the sequences of fuzzy sets and of join spaces determined (see [8])by all i.p.s. hypergroups of order seven. For the meaning ...

In this work, we study the signed Roman domination number of the join of graphs. Specially, we determine it for the join of cycles, wheels, fans, and friendship graphs.

We propose new families of graphs which exhibit quantum perfect state transfer. Our constructions are based on the join operator on graphs, its circulant generalizations, and the Cartesian product of graphs. We build upon the results of Bašić and Petković (Applied Mathematics Letters 22(10):1609-1615, 2009) and construct new integral circulants and regular graphs with perfect state transfer. Mo...

In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...