A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Liangsong Huang, Yu Hu, Yuxia Li, P. K. Kishore Kumar, Dipak Koley and Arindam Dey
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Liangsong Huang: Key Laboratory for Robot Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China
Yu Hu: Key Laboratory for Robot Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China
Yuxia Li: Key Laboratory for Robot Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China
P. K. Kishore Kumar: Information Technology Department, Al Musanna College of Technology, Sultanate of Oman 111, Oman
Dipak Koley: Department of Computer Application, Techno India Hooghly, Chinsurah 712101, West Bengal, India
Arindam Dey: Department of Computer Science and Engineering, Saroj Mohan Institute of Technology, Hooghly 712512, West Bengal, India

Mathematics, 2019, vol. 7, issue 6, 1-20

Abstract: Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m -highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m -highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h -morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

Keywords: neutrosophic graph; complete neutrosophic graph; bipartite neutrosophic graph; complement neutrosophic graph; road transport network; wireless multihop network and social network (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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