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Journal of Information and Optimization Sciences

(Since 1980)
Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

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Monthly Journal: Publishes theoretical and applied research on topics in information and optimization sciences.

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Journal of Information and Optimization Sciences
Open Access Research Article

Similar d– even vertex odd mean labeling of diverse graphs

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pp. 1365–1396Vol. 44Issue 7October 2023DOI: 10.47974/JIOS-1352XML
Received:
07 Sep 2022
Published Online:
19 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

Similar d–even vertex odd mean labelingRooted product operationToeplitz graphsPrism graph

Subject Classifications

(2020) 05C9005C78

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