On The Locating-Chromatic Numbers of Subdivisions of Friendship Graph

Brilly Maxel Salindeho, Hilda Assiyatun, Edy Tri Baskoro

Abstract


Let c be a k-coloring of a connected graph G and let pi={C1,C2,...,Ck} be the partition of V(G) induced by c. For every vertex v of G, let c_pi(v) be the coordinate of v relative to pi, that is c_pi(v)=(d(v,C1 ),d(v,C2 ),...,d(v,Ck )), where d(v,Ci )=min{d(v,x)|x in Ci }. If every two vertices of G have different coordinates relative to pi, then c is said to be a locating k-coloring of G. The locating-chromatic number of G, denoted by chi_L (G), is the least k such that there exists a locating k-coloring of G. In this paper, we determine the locating-chromatic numbers of some subdivisions of the friendship graph Fr_t, that is the graph obtained by joining t copies of 3-cycle with a common vertex, and we give lower bounds to the locating-chromatic numbers of few other subdivisions of Fr_t.


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DOI: https://doi.org/10.22342/jims.26.2.822.175-184

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Journal of the Indonesian Mathematical Society
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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