Rainbow degree-jump coloring of graphs

Title

Rainbow degree-jump coloring of graphs

Creator

Mphako-Banda E.G.; Kok J.; Naduvath S.

Description

In this paper, we introduce a new notion called the rainbow degree-jump coloring of a graph. For a vertex v ? V(G), let the degree-jump closed neighbourhood of this vertex be defined as Ndeg [v] = {u: d(v, u) ? d(v)}. A proper coloring of a graph G is said to be a rainbow degree-jump coloring of G if for all v in V(G), c(Ndeg [v]) contains at least one of each color class. We determine a necessary and sufficient condition for a graph G to permit a rainbow degree-jump coloring. We also determine the rainbow degree-jump chromatic number, denoted by ?rdj (G), for certain classes of cycle related graphs. Mphako-Banda E.G., Kok J., Naduvath S., 2021.

Source

Carpathian Mathematical Publications, Vol-13, No. 1, pp. 229-239.

Date

2021-01-01

Publisher

Precarpathian National University

Subject

Blind vertex; Moore bound; Mphako graph; Rainbow degree-jump chromatic number; rainbow degree-jump coloring

Coverage

Mphako-Banda E.G., School of Mathematical Sciences, University of Witswatersrand, Johannesburg, South Africa; Kok J., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, India; Naduvath S., Department of Mathematics, CHRIST (Deemed to be University), Bangalore, Karnataka, India

Rights

All Open Access; Gold Open Access

Relation

ISSN: 20759827

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.15330/cmp.13.1.229-239

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85110411262&doi=10.15330%2fcmp.13.1.229-239&partnerID=40&md5=661156f3efb31ca07a3ac70baf69a1df