Locating Chromatic Number for Corona Operation of Path and Cycle

Nur Hamzah, A. Asmiati, Wahyu Dwi Amansyah

Abstract


The locating chromatic number (lcn) of a graph is a part of discrete mathematic research, there is no general theorem for determining the lcn of any graph. The corona operation of Pn and Cm, denoted by Pn⊙Cm is defined as the graph obtained by taking one copy of Pn and |V(Pn)| copies of Cm and then joining all the vertices of the kth-copy of Cm with the kth-vertex of Pn. In this paper, we discuss the lcn for the corona operation of path and cycle. The lcn of (Pn⊙C3) is 5 for 3 ≤n< 7 and 6 for n≥7. Moreover, the lcn of (Pn⊙C4) is 5 for 3≤n< 6 and 6 for n≥6

Keywords


Locating Chromatic Number, Corona Operation, Path, Cycle

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DOI: http://dx.doi.org/10.19184/ijc.2024.8.2.6

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