Near Mean Labeling in Dicyclic Snakes

K Palani, A Shunmugapriya

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.

Keywords


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

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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.




DOI: http://dx.doi.org/10.23755/rm.v45i0.1022

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