Produtos de Grafos Z_m-bem-cobertos

Márcia Rodrigues Cappelle Santana, Rommel Melgaço Barbosa

Abstract


Um grafo é $Z_m$-bem-coberto se $|I| \equiv |J|$ (mod m), $m\geq 2,$ para todo $I$, $J$ conjuntos independentes maximais em $V(G)$. Um grafo $G$ é fortemente $Z_m$-bem-coberto se $G$ é um grafo $Z_m$-bem-coberto e $G\backslash \{e\}$ é $Z_m$-bem-coberto, $\forall e \in E(G)$. Um grafo $G$ é $1$-$Z_m$-bem-coberto se $G$ é $Z_m$-bem-coberto e $G\backslash \{v\}$ é $Z_m$-bem-coberto, $\forall v \in V(G)$. Mostramos que os grafos $1$-$Z_m$-bem-cobertos, bem como os fortemente $Z_m$-bem-cobertos, com exceção de $K_1$ e $K_2$, têm cintura $ \leq 5$. Mostramos uma condição necessária e suficiente para que produtos lexicográficos de grafos sejam $Z_m$-bem-cobertos e algumas propriedades para o produto cartesiano de ciclos.

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DOI: https://doi.org/10.5540/tema.2012.013.01.0075

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