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Oblong Mean Prime Labeling and Oblong Difference Mean Prime Labeling of Complete Graphs and Complete Multipartite Graphs


Affiliations
1 Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamil Nadu, India
 

The oblong numbers are in the form n(n+1), where n = 1,2, . . . . i.e., the oblong numbers are 2, 6, 12, . . . . If the vertices of the given graph G are labeled with oblong numbers and the edges of the graph are labeled with mean of the labels at the end vertices then G is said to have Oblong Mean Prime Labeling (OMPL). Similarly, if the vertices of G are labeled with oblong numbers and the edges of the graphs are labeled with mean of the absolute difference of the labels at the end vertices then G is said to have Oblong Difference Mean Prime Labeling (ODMPL). In this paper, the Oblong Mean Prime Labeling and Oblong Difference Mean Prime Labeling of Complete Graphs (CGs) Kn, n≥3 and Complete Multipartite Graphs (CMGs), K n n n n i 1 2 t 1 , , , , where 1i t ≤ ≤ have been investigated and obtained the results for such graphs.

Keywords

Complete Graphs (CGs) and Complete Multipartite Graphs (CMGs), Oblong Difference Mean Prime Labeling(ODMPL), Oblong Mean Prime Labeling (OMPL)
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  • Bondy JA, Murty USR. Graph Theory with Applications. New York: Elseveir Science Publishing Co., Inc; 1976. https://doi.org/10.1007/978-1-349-03521-2

  • Chih - Hung Yen. On r - Equitable Coloring of Complete Multipartite Graphs. Taiwanese Journal of Mathematics. 2013; 17(3):1–8. https://doi.org/10.11650/tjm.17.2013.2666

  • Gallian JA. A dynamic survey of graph labeling. The Electronic Journal of Combinatorics. 2009; 16:DS6.

  • Mathew Varkey TK, Sunoj BS. Oblong Mean Prime Labeling of some cycle graphs. Advances in Dynamical Systems and Applications. 2017; 12(2):181–6.

  • Mathew Varkey TK, Sunoj BS. Oblong Difference Mean Prime Labeling of some cycle graphs. International Journal of Statistics and Systems. 2017; 12(2):285–92.

  • Mathew Varkey TK, Sunoj BS. Oblong Mean Prime Labeling of some snake graphs. International Journal on Recent and Innovation Trends in Computing and Communication. 2017; 5(6):5–7.

  • Mathew Varkey TK, Sunoj BS. Oblong Difference Mean Prime Labeling of some cycle graphs. Anveshana’s International Journal of Reseach in Engineering and Applied Sciences. 2018; 3(2):78–81.

  • Neville Robbins, Beginning Numbereory, Narosa Publishing House Pvt. Ltd., Reprint 2006.


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  • Oblong Mean Prime Labeling and Oblong Difference Mean Prime Labeling of Complete Graphs and Complete Multipartite Graphs

Abstract Views: 338  |  PDF Views: 154

Authors

P. Hemalatha
Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamil Nadu, India
V. Sudha
Department of Mathematics, Vellalar College for Women, Erode – 638 012, Tamil Nadu, India

Abstract


The oblong numbers are in the form n(n+1), where n = 1,2, . . . . i.e., the oblong numbers are 2, 6, 12, . . . . If the vertices of the given graph G are labeled with oblong numbers and the edges of the graph are labeled with mean of the labels at the end vertices then G is said to have Oblong Mean Prime Labeling (OMPL). Similarly, if the vertices of G are labeled with oblong numbers and the edges of the graphs are labeled with mean of the absolute difference of the labels at the end vertices then G is said to have Oblong Difference Mean Prime Labeling (ODMPL). In this paper, the Oblong Mean Prime Labeling and Oblong Difference Mean Prime Labeling of Complete Graphs (CGs) Kn, n≥3 and Complete Multipartite Graphs (CMGs), K n n n n i 1 2 t 1 , , , , where 1i t ≤ ≤ have been investigated and obtained the results for such graphs.

Keywords


Complete Graphs (CGs) and Complete Multipartite Graphs (CMGs), Oblong Difference Mean Prime Labeling(ODMPL), Oblong Mean Prime Labeling (OMPL)

References





DOI: https://doi.org/10.15613/sijrs%2F2019%2Fv6i2%2F209463