Sum Labeling for Some Star and Cycle Related Special Graphs

A sum labeling is a mapping from the vertices of G into the positive integers such that, for any two vertices u, v V (G) with labels (u) and (v), respectively, (uv) is an edge iff (u) + (v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is known as the sum number of the graph. In this paper, we will obtain optimal sum labeling scheme for some star and cycle related special graphs

BALANCED HESITANCY FUZZY GRAPHS

In this paper, a new Hesitancy Fuzzy Graph Model called Balanced Hesitancy Fuzzy Graphs (BHFGs) is introduced. Also, we discuss the various concepts related with Balanced Hesitancy Fuzzy Graphs with their graphical representations. Further we develop the concept of self complementary hesitancy fuzzy graphs along with the theoretical illustration