Open Access
Research Article
Similar d– even vertex odd mean labeling of diverse graphs
*Mohamed R. Zeen El DeenCorresponding authormohamed.zeeneldeen@sci.suezuni.edu.egDepartment of Mathematics and Computer Science Faculty of Science Suez UniversitySuez, 43221, EgyptView full profile → , Nora A. Omaralaa.nora99@yahoo.comDepartment of Mathematics and Computer Science Faculty of Science Port-Said UniversityEgyptView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 Sep 2022
- Published Online:
- 11 Oct 2023
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1352
- Pages:
- 1365–1396
Abstract
An injective function F where, F : V(G) → {0,2,4, ..., 2b + 2d - 2} is said to be d-even vertex odd mean labeling (d-EVOML) of the graph G(a, b) when the induced mapping F* : E(G) → {1,3, ..., 2b - 1} given by: F*(lw) = F(l)+F(w)/2, is a bijective function. A d - even vertex odd mean graph is a graph which allows even vertex odd mean labelling. In this study, we identify the lowest value of d for which the graphs: Y-tree, star graph, Px ʘ Kh, crown graph Rh, and rooted product Ph◊C4 have a d- even vertex odd mean labeling. Furthermore, we find the minimum number d for which the graphs: cycle graph Ch when h ≡ 2 mod 4, dragon graph Px(Ch) when h ≡ 2 mod 4, x ≥ 1, prism graph Ph, and Toeplitz graphs Th(1, 3), Th(1, 5) and Th(1, 3, 5) have a similar d- even vertex odd mean labeling. In the end, we establish that no odd cycle Ch is an even vertex odd mean graph for all d.
Keywords
Subject Classifications
(2020) 05C9005C78
References
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