PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$
Abstract
Given a graph $G$ and a positive integer $i,$ an $i$-packing in $G$ is a subset $X$ of $V(G)$ such that the distance $d_G(u, v)$ between any two distinct vertices $u,v\,\in\,X$ is greater than $i.$ The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest integer $k$ such that the vertex set of $G$ can be partitioned into sets $V_i,$ $i\in [k],$ where each $V_i$ is an $i$-packing. In this paper, we determine the packing chromatic number of the corona products of paths and cycles of small order (at most $11$ vertices) with an edge and obtain bounds for the packing chromatic number of corona products of paths and cycles of larger order with an edge.
Keywords
Thanks
The authors would like to thank the referee for suggestions which improved the presentation of the paper.
References
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Details
Primary Language
English
Subjects
Combinatorics and Discrete Mathematics (Excl. Physical Combinatorics)
Journal Section
Research Article
Publication Date
January 8, 2026
Submission Date
December 17, 2024
Acceptance Date
April 27, 2025
Published in Issue
Year 2026 Volume: 16 Number: 1
APA
R. Sampathkumar, R. S., Sivakaran, T., & Unnikrishnan, R. (2026). PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$. TWMS Journal of Applied and Engineering Mathematics, 16(1), 94-108. https://izlik.org/JA87RY76KZ
AMA
1.R. Sampathkumar RS, Sivakaran T, Unnikrishnan R. PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$. JAEM. 2026;16(1):94-108. https://izlik.org/JA87RY76KZ
Chicago
R. Sampathkumar, R. Sampathkumar, T. Sivakaran, and R. Unnikrishnan. 2026. “PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$”. TWMS Journal of Applied and Engineering Mathematics 16 (1): 94-108. https://izlik.org/JA87RY76KZ.
EndNote
R. Sampathkumar RS, Sivakaran T, Unnikrishnan R (January 1, 2026) PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$. TWMS Journal of Applied and Engineering Mathematics 16 1 94–108.
IEEE
[1]R. S. R. Sampathkumar, T. Sivakaran, and R. Unnikrishnan, “PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$”, JAEM, vol. 16, no. 1, pp. 94–108, Jan. 2026, [Online]. Available: https://izlik.org/JA87RY76KZ
ISNAD
R. Sampathkumar, R. Sampathkumar - Sivakaran, T. - Unnikrishnan, R. “PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$”. TWMS Journal of Applied and Engineering Mathematics 16/1 (January 1, 2026): 94-108. https://izlik.org/JA87RY76KZ.
JAMA
1.R. Sampathkumar RS, Sivakaran T, Unnikrishnan R. PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$. JAEM. 2026;16:94–108.
MLA
R. Sampathkumar, R. Sampathkumar, et al. “PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 1, Jan. 2026, pp. 94-108, https://izlik.org/JA87RY76KZ.
Vancouver
1.R. Sampathkumar R. Sampathkumar, T. Sivakaran, R. Unnikrishnan. PACKING COLORINGS OF THE CORONA PRODUCT OF THE PATH $P_n$ AND THE CYCLE $C_n$ WITH AN EDGE $K_2$. JAEM [Internet]. 2026 Jan. 1;16(1):94-108. Available from: https://izlik.org/JA87RY76KZ