Near Mean Labeling in Dicyclic Snakes

Authors

  • K Palani A.P.C. Mahalaxmi College for Women, Thoothukudi-628 002, Tamil Nadu, India)
  • A Shunmugapriya Department of Mathematics, Sri Sarada College for Women (Autonomous), Tirunelveli-627 011. (Research scholar-19122012092005, A.P.C. Mahalaxmi College for Women, Thoothukudi-628 002, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, Tamil Nadu, India)

DOI:

https://doi.org/10.23755/rm.v45i0.1022

Keywords:

Near mean, labeling, digraphs, di-cyclic, di-Quadrilateral, di-Pentagonal, snake.

Abstract

K. Palani et al. defined the concept of near mean labeling in digraphs. Let D=(V,A) be a digraph where Vthe vertex is set and A is the arc set. Let f:V\rightarrow{0,\ 1,\ 2,\ \ldots,q} be a 1-1 map. Define f^\ast:A\rightarrow{1,\ 2,\ \ldots,q} byf^\ast\left(e=\vec{uv}\right)=\left\lceil\frac{f\left(u\right)+f(v)}{2}\right\rceil. Letf^\ast\left(v\right)=\left|\sum_{w\in V}{f^\ast(\vec{vw})}-\sum_{w\in V}{f^\ast(\vec{wv})}\right|. Iff^\ast\left(v\right)\le2\ \ \forall\ v\in A(D), then f is said to be a near mean labeling of D and D is said to be a near mean digraph. In this paper, different dicyclic snakes are defined and the existence of near mean labeling in them is checked.

References

Gallian J A, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics 17(2014)

Harary F, Graph Theory, Addition Wesley, Massachusetts(1972).

Palani K and Shunmugapriya A, “Near Mean Labeling in Dragon Digraphs”, Journal of Xidian University, Vol 14, Issue 3, pp. 1298-1307, 2020.

PonrajR and Somasundaram S, “Mean labeling of graphs”, National Academy of Science Letters Vol.26, p210-213, 2003.

Raval K K and Prajapati U M, “Vertex even and odd mean labeling in the context of some cyclic snake graphs”, Journal of Emerging Technologies and Innovative Research(JETIR), Vol 4, Issue 6, Sep 2017.

Rosa A, 1967. On certain valuations of the vertices of a graph, Theory of Graphs(Intl. Symp. Rome 1966), Gordon and Breach, Dunod, Paris, 349-355.

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Published

2023-01-30

Issue

Vol. 45 (2023): Special Issue: Advances in Applied and Intellectual Mathematics

Section

Volume 44-2022

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