L(t, 1)-colouring of graphs

Title

L(t, 1)-colouring of graphs

Creator

Pandey P.; Kureethara J.V.

Description

One of the most famous applications of Graph Theory is in the field of Channel Assignment Problems. There are varieties of graph colouring concepts that are used for different requirements of frequency assignments in communication channels. We introduce here L(t, 1)-colouring of graphs. This has its foundation in T-colouring and L(p, q)-colouring. For a given finite set T including zero, an L(t, 1)-colouring of a graph G is an assignment of non-negative integers to the vertices of G such that the difference between the colours of adjacent vertices must not belong to the set T and the colours of vertices that are at distance two must be distinct. The variable t in L(t, 1) denotes the elements of the set T. For a graph G, the L(t, 1)-span of G is the minimum of the highest colour used to colour the vertices of a graph out of all the possible L(t, 1)-colourings. It is denoted by ?t,1(G). We study some properties of L(t, 1)-colouring. We also find upper bounds of ?t,1(G) of stars and multipartite graphs. I??k University, Department of Mathematics, 2022; all rights reserved.

Source

Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, Vol-12, No. 1, pp. 296-301.

Date

2022-01-01

Publisher

Isik University

Subject

1)-colouring; Colour span; Communication networks; L(t; Radio frequency

Coverage

Pandey P., Department of Mathematics, Christ University, Bengaluru, 560029, India; Kureethara J.V., Department of Mathematics, Christ University, Bengaluru, 560029, India

Rights

Restricted Access

Relation

ISSN: 21461147

Format

Online

Language

English

Type

Article

Identifier

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85123542319&partnerID=40&md5=9034abce9eb4faac9e1b1356402c679d