On Dominating Energy in Bipolar Single-Valued Neutrosophic Graph

Abstract

: One of the most important concepts in graph theory for dealing with unpredictable
phenomena is the concept of domination and it has gained attention from many scholars. Recently,
dominating energy of graph plays a vital role in the field of graph energies. If the fuzzy graph (FG)
fails to give outstanding results, the neutrosophic set (NS) and neutrosophic graphs (NG) can
handle the uncertainty correlated with indeterminate and inconsistent information in any
real-world scenario. Recent studies related to domination energy in fuzzy environment only deal
with the single membership function. It is more flexible and applicable to use bipolar neutrosophic
models because they include both positive and negative influencers. Therefore, this paper is based
on some developments of neutrosophic graph theory to deal with situations where imprecision is
characterized by positive and negative types of membership functions. A novel concept of the
dominating energy graph is proposed based on recently introduced concept of bipolar
single-valued neutrosophic graphs (BSVNG). Moreover, this study analyses the concepts of
dominating energy graph in BSVNG environment. More precisely, the adjacency matrix of a
dominating BSVNG as well as the spectrum of the adjacency matrix and their related theory is
developed with the help of illustrative examples. Further, the domination energy of BSVNG is
computed. Aside from it, various operations relating to this dominating have been depicted. The
complement, union, and join of dominating energy in BSVNG have been investigated by using
appropriate examples and some properties of the dominating energy in BSVNG are established.