The Bounds on the Locating-Chromatic Number for a Subdivision of a Graph on One Edge | Zendy

Ira Apni Purwasih | Zendy; Edy Tri Baskoro | Zendy; Hilda Assiyatun | Zendy; Djoko Suprijanto | Zendy

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The Bounds on the Locating-Chromatic Number for a Subdivision of a Graph on One Edge

Author(s) -

Ira Apni Purwasih,

Edy Tri Baskoro,

Hilda Assiyatun,

Djoko Suprijanto

Publication year - 2015

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2015.12.080

Subject(s) - subdivision , chromatic scale , graph , computer science , upper and lower bounds , enhanced data rates for gsm evolution , combinatorics , friendship graph , discrete mathematics , mathematics , line graph , artificial intelligence , voltage graph , geography , mathematical analysis , archaeology

The study of locating-chromatic numbers has been done for many classes of graphs. Recently, Behtoei and Anbarloei (2014) presented the locating-chromatic number of wheels. Inspired by the result of Behtoei and Anbarloei, the authors (2012,2013) gave the locating-chromatic number of the subdivision of a wheel on one of its spoke or cycle edges. In this paper, we determine an upper bound on the locating-chromatic number of a subdivision of any connected graph on any one edge and show that the bound is tight. In particular, we give the lower bound for the locating-chromatic number of a subdivision of any graph on a pendant edge. Furthermore, we give the exact values of the locating-chromatic number of a subdivision of a complete and a star graph on any one edge

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