Connected k-forcing sets of graphs and splitting graphs

Title

Connected k-forcing sets of graphs and splitting graphs

Creator

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

Description

The notion of k-forcing number of a graph was introduced by Amos et al. For a given graph G and a given subset I of the vertices of the graph G, the vertices in I are known as initially colored black vertices and the vertices in V (G) ? I are known as not initially colored black vertices or white vertices. The set I is a k-forcing set of a graph G if all vertices in G eventually colored black after applying the following color changing rule: If a black colored vertex is adjacent to at most k-white vertices, then the white vertices change to be colored black. The cardinality of a smallest k-forcing set is known as the k-forcing number Zk (G) of the graph G. If the sub graph induced by the vertices in I are connected, then I is called the connected k-forcing set. The minimum cardinality of such a set is called the connected k-forcing number of G and is denoted by Zck (G). This manuscript is intended to study the connected k-forcing number of graphs and the splitting graphs. 2020 the author(s).

Source

Journal of Mathematical and Computational Science, Vol-10, No. 3, pp. 656-680.

Date

2020-01-01

Publisher

SCIK Publishing Corporation

Subject

Connected k-forcing number; K-forcing number; Zeroforcing number

Coverage

Premodkmuar K.P., 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., 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/4446

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