Even-Odd Cordial Labeling on Join of Zero Divisor Graphs

S. Naresh kumar; D. Bharathi

doi:https://doi.org/10.14445/22315373/IJMTT-V72I7P107

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 7 | Year 2026 | Article Id. IJMTT-V72I7P107 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I7P107

Even-Odd Cordial Labeling on Join of Zero Divisor Graphs

S. Naresh kumar, D. Bharathi

Received	Revised	Accepted	Published
29 May 2026	03 Jul 2026	20 Jul 2026	31 Jul 2026

Citation :

S. Naresh kumar, D. Bharathi, "Even-Odd Cordial Labeling on Join of Zero Divisor Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 7, pp. 53-68, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I7P107

Abstract

Let G(V,E) be a graph, and let f: V(G) →{1,2,….|𝑉(𝐺)|} be a bijective vertex labeling. The induced edge labeling f*: E(G) → {0,1} is defined by assigning the label 1 to an edge uv whenever the labels f(u) and f(v) have same parity, and the label 0 whenever they have different parities. If the difference between the number of edges labeled 0 and the number of edges labeled 1 is at most one, then f is called an even – odd cordial labeling (EOCL). A graph that admits such a labeling is known as an even – odd cordial Graph (EOCG). In this work, we study the existence of even – odd cordial labeling for the join of zero – divisor graphs, namely Γ(𝑍𝑛𝑝) + Γ(𝑍4) , Γ(𝑍𝑛𝑝) + Γ(𝑍6) , and Γ(𝑍𝑛𝑝) + Γ(𝑍9) ( for n = 2,3,5). The results establish conditions under which these graph families satisfy the requirements of even – odd cordial labeling, thereby extending the study of cordial labeling s to joins of zero – divisor graphs.

Keywords

Cordial labeling, Even-Odd cordial labeling, Zero divisors,Zero - divisor graphs.

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