DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2023): 0.5

5-year Journal Impact Factor (2023): 0.6

CiteScore (2023): 2.2

SNIP (2023): 0.681

Discussiones Mathematicae Graph Theory

Article in press

Authors:

A. Ghanbari

Ali Ghanbari

Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran
Babolsar, Iran
e-mail: ali.ghanbari239@gmail.com
and
Doost Ali Mojdeh 2
Department of Mathematics
Faculty of Mathematical Sciences
University of Mazandaran
Babolsar, Iran

email: ali.ghanbari239@gmail.com

D.A. Mojdeh

Doost Ali Mojdeh

Department of Mathematics, Faculty of Mathematical Sciences
University of Mazandaran, Babolsar, Iran

email: damojdeh@umz.ac.ir

0000-0001-9373-3390

Title:

On two conjectures regarding the neighbor-locating chromatic number

PDF

Source:

Discussiones Mathematicae Graph Theory

Received: 2024-07-06 , Revised: 2024-11-17 , Accepted: 2024-11-17 , Available online: 2024-12-06 , https://doi.org/10.7151/dmgt.2572

Abstract:

In the paper (Discussiones Mathematicae Graph Theory 43 (2023) 659–675) has been posed two conjectures on neighbor-locating coloring of graphs. In this paper, we disprove one of them by presenting a family of counterexamples and prove the another one.

Keywords:

coloring, neighbor-locating coloring, conjectures

References:

  1. L. Alcón, M. Gutierrez, C. Hernando, M. Mora and I.M. Pelayo, Neighbor-locating colorings in graphs, Theoret. Comput. Sci. 806 (2020) 144–155.
    https://doi.org/10.1016/j.tcs.2019.01.039
  2. L. Alcón, M. Gutierrez, C. Hernando, M. Mora and I.M. Pelayo, The neighbor-locating-chromatic number of trees and unicyclic graphs, Discuss. Math. Graph Theory 43 (2023) 659–675.
    https://doi.org/10.7151/dmgt.2392
  3. A. Behtoei and M. Anbarloei, A bound for the locating chromatic numbers of trees, Trans. Comb. 4 (2015) 31–41.
    https://doi.org/10.22108/toc.2015.6024
  4. A. Behtoei and M. Anbarloei, The locating chromatic number of the join of graphs, Bull. Iranian Math. Soc. 40 (2014) 1491–1504.
  5. A. Behtoei and B. Omoomi, On the locating chromatic number of the Cartesian product of graphs, Ars Combin. 126 (2016) 221–235.
  6. G. Chartrand, D. Erwin, M.A. Henning, P.J. Slater and P. Zhang, The locating-chromatic number of a graph, Bull. Inst. Combin. Appl. 36 (2002) 89–101.
  7. A. Ghanbari and D.A. Mojdeh, Neighbor locating coloring on graphs: Three products, J. Combin. Math. Combin. Comput. 122 (2024) 73–89.
    https://doi.org/10.61091/jcmcc122-06
  8. C. Hernando, M. Mora, I.M. Pelayo, L. Alcón and M. Gutierrez, Neighbor-locating coloring: graph operations and extremal cardinalities, Electron. Notes Discrete Math. 68 (2018) 131–136.
    https://doi.org/10.1016/j.endm.2018.06.023
  9. M. Korivand, D.A. Mojdeh, E.T. Baskoro and A. Erfanian, Edge-locating coloring of graphs, Electron. J. Graph Theory Appl. (EJGTA) 12 (2024) 55–73.
    https://doi.org/10.5614/ejgta.2024.12.1.6
  10. D.A. Mojdeh, On the conjectures of neighbor locating coloring of graphs, Theoret. Comput. Sci. 922 (2022) 300–307.
    https://doi.org/10.1016/j.tcs.2022.04.031
  11. D.B. West, Introduction to Graph Theory (Second Edition) (Prentice Hall, USA, 2001).
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