On Arithmetic Cordial Labeling of Some Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909006110392320 |
|---|---|
| author | Andoyo, Jason D. Prudencio, Jemina Clarisse C. Rulete, Ricky F. |
| author_facet | Andoyo, Jason D. Prudencio, Jemina Clarisse C. Rulete, Ricky F. |
| contents | Let $η$ be a fixed positive integer. Let $S$ be a subset of $\mathbb{Z}$, $\star:S\times S\to \mathbb{Z}$ be a binary function, and $ζ_η:\{ξ\in \mathbb{Z}:\gcd(ξ,η)=1\}\to \{0,1\}$ be a function. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to S$ (where $|S|=n$) is called an arithmetic cordial labeling modulo $η$ under $\langle S,ζ_η,\star\rangle$ if the induced function $f_η^*:E(G)\to \{0,1\}$, defined by $f_η^*(uv)=0$ whenever $ζ_η(f(a)\star f(b))=0$ or $\gcd(f(a)\star f(b),η)\neq 1$, and $f_η^*(uv)=1$ whenever $ζ_η(f(a)\star f(b))=1$, satisfies the condition $|e_{f_η^*}(0)-e_{f_η^*}(1)|\leq 1$, where $e_{f_η^*}(i)$ is the number of edges with label $i$ ($i=0,1$). In this paper, we explore the arithmetic cordial labeling of some graphs under conditions imposed on the function $ζ_η$. The graphs included are star graphs, ladder graphs, alternate cycle snake graphs, join graphs, corona graphs, and tensor product graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Arithmetic Cordial Labeling of Some Graphs Andoyo, Jason D. Prudencio, Jemina Clarisse C. Rulete, Ricky F. Combinatorics 05C76, 05C78, 11A05, 11A07 Let $η$ be a fixed positive integer. Let $S$ be a subset of $\mathbb{Z}$, $\star:S\times S\to \mathbb{Z}$ be a binary function, and $ζ_η:\{ξ\in \mathbb{Z}:\gcd(ξ,η)=1\}\to \{0,1\}$ be a function. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to S$ (where $|S|=n$) is called an arithmetic cordial labeling modulo $η$ under $\langle S,ζ_η,\star\rangle$ if the induced function $f_η^*:E(G)\to \{0,1\}$, defined by $f_η^*(uv)=0$ whenever $ζ_η(f(a)\star f(b))=0$ or $\gcd(f(a)\star f(b),η)\neq 1$, and $f_η^*(uv)=1$ whenever $ζ_η(f(a)\star f(b))=1$, satisfies the condition $|e_{f_η^*}(0)-e_{f_η^*}(1)|\leq 1$, where $e_{f_η^*}(i)$ is the number of edges with label $i$ ($i=0,1$). In this paper, we explore the arithmetic cordial labeling of some graphs under conditions imposed on the function $ζ_η$. The graphs included are star graphs, ladder graphs, alternate cycle snake graphs, join graphs, corona graphs, and tensor product graphs. |
| title | On Arithmetic Cordial Labeling of Some Graphs |
| topic | Combinatorics 05C76, 05C78, 11A05, 11A07 |
| url | https://arxiv.org/abs/2602.22526 |