On the Locating Chromatic Number of Barbell Shadow Path Graph

A. Asmiati, Maharani Damayanti, Lyra Yulianti

Abstract


The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.

Keywords


the locating-chromatic number, shadow path graph, barbell graph

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DOI: http://dx.doi.org/10.19184/ijc.2021.5.2.4

References

Asmiati, H. Assiyatun and E.T. Baskoro, Locating-chromatic number of amalgamation of stars, ITB J. Sci., 43 (1)(2011), 1 -- 8.

Asmiati, On the locating-chromatic number of non-homogeneous caterpillars and firecracker graphs, Far East J. Math. Sci., 100 (2016), No.8, 1305 -- 1316.

Asmiati, I. Ketut S. G. Y. and L. Yulianti, On the locating chromatic number of certain barbell graphs, Int. J. Math. Math. Sci., 2018 (2018), 1 -- 5.

D. K. Sofyan, E. T. Baskoro, and H. Assiyatun, On the locating chromatic number of homogeneous lobster, AKCE Int. J. Graphs Comb., 10 (2013), no. 3, 245 -- 252.

D. Welyyanti, E. T. Baskoro, R. Simanjuntak and S. Uttunggadewa, On the locating chromatic number of complete n-ary tree, AKCE Int. J. Graphs Comb., 10 (2013), no.3, 309 - -315.

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.

G. Chartrand, D. Erwin, M. A. Henning, P. J. Slater, and P. Zhang, Graphs of order n-1, Discrete Math., 269 (2003), no. 1-3, 65 -- 79.

M. Ghanem, H. Al-Ezeh, A. Dabour. Locating chromatic number of powers of path and cycles, Symmetry 11, 389 (2019), 2 -- 6.


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