On Legendre Cordial Labeling of Complete Graphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908533122924544 |
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| author | Andoyo, J. D. |
| author_facet | Andoyo, J. D. |
| contents | Let $p$ be an odd prime. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\ldots,n\}$ is said to be a Legendre cordial labeling modulo $p$ if the induced function $f_p^*:E(G)\to \{0,1\}$, defined by $f_p^* (uv)=0$ whenever $([f(u)+f(v)]/p)=-1$ or $f(u)+f(v)\equiv 0(\text{mod } p)$ and $f_p^* (uv)=1$ whenever $([f(u)+f(v)]/p)=1$, satisfies the condition $|e_{f_p^*}(0)-e_{f_p^*}(1)|\leq 1$ where $e_{f_p^*}(i)$ is the number of edges with label $i$ ($i=0,1$). This paper explores the characterization of the Legendre cordial labeling modulo $p$ of the complete graph $K_n$ using the concept of Legendre graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09528 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Legendre Cordial Labeling of Complete Graphs Andoyo, J. D. Combinatorics 05C78 (Primary), 11A07, 11A15 (Secondary) Let $p$ be an odd prime. For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\ldots,n\}$ is said to be a Legendre cordial labeling modulo $p$ if the induced function $f_p^*:E(G)\to \{0,1\}$, defined by $f_p^* (uv)=0$ whenever $([f(u)+f(v)]/p)=-1$ or $f(u)+f(v)\equiv 0(\text{mod } p)$ and $f_p^* (uv)=1$ whenever $([f(u)+f(v)]/p)=1$, satisfies the condition $|e_{f_p^*}(0)-e_{f_p^*}(1)|\leq 1$ where $e_{f_p^*}(i)$ is the number of edges with label $i$ ($i=0,1$). This paper explores the characterization of the Legendre cordial labeling modulo $p$ of the complete graph $K_n$ using the concept of Legendre graph. |
| title | On Legendre Cordial Labeling of Complete Graphs |
| topic | Combinatorics 05C78 (Primary), 11A07, 11A15 (Secondary) |
| url | https://arxiv.org/abs/2509.09528 |