Two distance forcing number of a graph

Title

Two distance forcing number of a graph

Creator

Premodkumar K.P.; Dominic C.; Chacko B.

Description

Motivated from the graph parameters namely zero forcing number, k-forcing number and the connected k-forcing number, in this article, we introduce a new parameter known as the 2-distance forcing number. Assume that each vertex of a graph G = (V (G), E(G)) is colored as either white or black. Consider the set Z2d of black colored vertices of the graph G. The color change rule changes the color of a white vertex v to black if the white vertex v is the only 2-distance white neighbor of a black vertex u. The set Z2d is called a two distance forcing set of G if all vertices of the graph G will be turned black after limited applications of the color change rule. The 2-distance forcing number of G, denoted by Z2d (G), is the minimum of | Z2d | over all 2-distance forcing sets Z2d ? V (G). This manuscript is intended to study the 2-distance forcing number of some graphs. We find the exact value of the 2-distance forcing number of graphs such as the pineapple graph, gear graph, jelly fish graph, helm graph, sunflower graph, comet graph and the n-pan graph. 2020 the author(s).

Source

Journal of Mathematical and Computational Science, Vol-10, No. 6, pp. 2233-2248.

Date

2020-01-01

Publisher

SCIK Publishing Corporation

Subject

2-distance forcing number; Diameter; Graph; K-forcing number

Coverage

Premodkumar K.P., P.G. Department and Research Center of Mathematics, St. Josephs College, Devagiri, Calicut, Kerala, India; Dominic C., Department of Mathematics, CHRIST(Deemed to be University), Karnataka, India; Chacko B., P.G. Department and Research Center of Mathematics, St. Josephs College, Devagiri, Calicut, Kerala, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 19275307

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.28919/jmcs/4842

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