Locating Chromatic Number for Corona Operation of Path and Cycle

Hamzah, Nur (Universitas Lampung)
Asmiati, A. (University of Lampung)
Amansyah, Wahyu Dwi (Universitas Lampung)

Indonesian Journal of Combinatorics
Vol 8, No 2 (2024)

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