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2019•Journal of the Indonesian Mathematical SocietyOpen access

Regularity Of Cubic Graph With Application

Kishore Kumar Krishna, Hossein Rashmanlou, Ali Asghar Talebi, Farshid Mofidnakhaei

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Abstract

A cubic graph is a generalized structure of a fuzzy graph that gives moreprecision, flexibility and compatibility to a system when compared with systems thatare designed using fuzzy graphs. In this paper, some properties of an edge regularcubic graph are given. Particularly, strongly regular, edge regular and bi-regularcubic graphs are defined and the necessary and sucient condition for a cubic graphto be strongly regular is studied. Likewise, we have introduced a partially edgeregular cubic graph and fully edge regular cubic graph with suitable illustrations.Finally, we gave an application of cubic digraph in travel time.

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What this paper is about

A cubic graph is a generalized structure of a fuzzy graph that gives moreprecision, flexibility and compatibility to a system when compared with systems thatare designed using fuzzy graphs. In this paper, some properties of an edge regularcubic graph are given. Particularly, strongly regular, edge regular and bi-regularcubic graphs are defined and the necessary and sucient condition for a cubic graphto be strongly regular is studied. Likewise, we have introduced a partially edgeregular cubic graph and fully edge regular cubic graph with suitable illustrations.Finally, we gave an application of cubic digraph in travel time.

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Available abstract

A cubic graph is a generalized structure of a fuzzy graph that gives moreprecision, flexibility and compatibility to a system when compared with systems thatare designed using fuzzy graphs. In this paper, some properties of an edge regularcubic graph are given. Particularly, strongly regular, edge regular and bi-regularcubic graphs are defined and the necessary and sucient condition for a cubic graphto be strongly regular is studied. Likewise, we have introduced a partially edgeregular cubic graph and fully edge regular cubic graph with suitable illustrations.Finally, we gave an application of cubic digraph in travel time.

Key concepts: Cubic graph, Mathematics, Foster graph, Symmetric graph, Digraph, Graph, Combinatorics, Strongly regular graph

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