On Legendre Cordial Labeling of Some Graphs Under Graph Opearations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918140576792576 |
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| author | Andoyo, Jason |
| author_facet | Andoyo, Jason |
| contents | For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\cdots,n\}$ is said to be a Legendre cordial labeling modulo $p$, where $p$ is an odd prime, 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 investigates the Legendre cordial labeling of graphs obtained through various operations: join, corona, lexicographic product, cartesian product, tensor product, and strong product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Legendre Cordial Labeling of Some Graphs Under Graph Opearations Andoyo, Jason Combinatorics 05C78, 11A07, 11A15 For a simple connected graph $G$ of order $n$, a bijective function $f:V(G)\to\{1,2,\cdots,n\}$ is said to be a Legendre cordial labeling modulo $p$, where $p$ is an odd prime, 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 investigates the Legendre cordial labeling of graphs obtained through various operations: join, corona, lexicographic product, cartesian product, tensor product, and strong product. |
| title | On Legendre Cordial Labeling of Some Graphs Under Graph Opearations |
| topic | Combinatorics 05C78, 11A07, 11A15 |
| url | https://arxiv.org/abs/2509.11012 |