Abstract
A single-valued neutrosophic set is an instance of a neutrosophic set, which provides us an additional possibility to represent uncertainty, imprecise, incomplete and inconsistent information existing in real situations. In this research study, we present concepts of energy, Laplacian energy and signless Laplacian energy in single-valued neutrosophic graphs (SVNGs), describe some of their properties and develop relationship among them. We also consider practical examples to illustrate the applicability of the our proposed concepts.
Highlights
Smarandache [1] originally introduced the notion of neutrosophic set (NS) from philosophical point of view
We present concepts of energy, Laplacian energy and signless Laplacian energy in single-valued neutrosophic graphs (SVNGs), describe some of their properties and develop relationship among them
We have introduced certain novel concepts, including energy, Laplacian energy and signless Laplacian energy of SVNGs
Summary
Smarandache [1] originally introduced the notion of neutrosophic set (NS) from philosophical point of view. Wang et al [2] put forth the notion of a single-valued neutrosophic set (SVNS) from a scientific or engineering point of view, as a subclass of the NS and an extension of intuitionistic fuzzy set (IFS) [3], and provide its various properties. Many generalized fuzzy graphs [21,22,23,24,25,26,27,28,29,30,31] have been introduced in literature Among these extensions, the notion of intuitionistic fuzzy graph (IFG) whose vertex set and edge set specify a degree of membership, a degree of non-membership and a degree of hesitancy was proposed by Parvathi and Karunambigai [21], and Akram and Davvaz [23]. We present concepts of energy, Laplacian energy and signless Laplacian energy in single-valued neutrosophic graphs (SVNGs), describe some of their properties and develop relationship among them. For more details and background, the readers are referred to [34,35,36,37,38,39,40]
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