Zero forcing number of degree splitting graphs and complete degree splitting graphs

Title

Zero forcing number of degree splitting graphs and complete degree splitting graphs

Creator

Dominic C.

Description

A subset Z V(G) of initially colored black vertices of a graph G is known as a zero forcing set if we can alter the color of all ver- tices in G as black by iteratively applying the subsequent color change condition. At each step, any black colored vertex has exactly one white neighbor, then change the color of this white vertex as black. The zero forcing number Z(G), is the minimum number of vertices in a zero forcing set Z of G (see [11]). In this paper, we compute the zero forcing num- ber of the degree splitting graph (DS-Graph) and the complete degree splitting graph (CDS-Graph) of a graph. We prove that for any simple graph, Z[DS(G)] k + t, where Z(G) = k and t is the number of newly introduced vertices in DS(G) to construct it. 2019 Sciendo. All rights reserved.

Source

Acta Universitatis Sapientiae, Mathematica, Vol-11, No. 1, pp. 40-53.

Date

2019-01-01

Publisher

Sciendo

Subject

splitting graph; zero forcing number

Coverage

Dominic C., Department of Mathematics, CHRIST (Deemed to Be University), Bangalore, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 18446094

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.2478/ausm-2019-0004

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