Distance Degree Sequence and Distance Neighborhood Degree Sequence of Vertices of Drastic Sum of two Fuzzy Graphs on Stars

The distance degree sequence and distance neighborhood degree sequence are two sequences in fuzzy graphs. In graph theory, the distance degree sequence of a vertex involves the concept of the number of vertices at various distances from the given vertex of a graph. The concept of distance degree sequence of a vertex in fuzzy graph is developed by taking into account the membership values of the edges which are incident on the vertices at various distances from the given vertex of fuzzy graphs, and the distance neighborhood degree sequence considers the membership values of the vertices at various distances. The drastic sum of fuzzy graphs is an operation in fuzzy graph theory, which is the extension of the standard operations on graphs using the drastic sum of fuzzy sets. The drastic sum provides a way to combine two fuzzy graphs into a new fuzzy graph by using a specific rule for combining the membership values of edges and vertices between two fuzzy graphs. In this paper, the distance degree sequence and distance neighborhood degree sequence of the vertices in the drastic sum of two fuzzy graphs on star graphs are obtained in terms of the parameters of the given graphs by considering all possible cases of drastic sum in detail.