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On product-cordial index sets of Möbius ladders and their bridge join with $$K_4$$. (English) Zbl 1334.05147
Summary: Let $$G$$ be a simple graph, and let $$\mathbb{Z}_2=\{0,1\}$$ be the field with two elements. Any vertex labeling $$f:V(G)\to\mathbb{Z}_2$$ induces an edge labeling $$f^\star:E(G)\to\mathbb{Z}_2$$ defined by $$f^\ast(xy)=f(x)f(y)$$ for any edge $$xy\in E(G)$$. For each $$i\in\mathbb{Z}_2$$, define $$v_f(i)=|f^{-1}(i)|$$, and $$e_{f^\ast}(i)=|f^{\ast-1}(i)|$$. The product-cordial index set of a graph $$G$$ is defined as the set of possible values of $$|e_{f^\ast}(0)-e_{f^\ast}(1)|$$ taken over all labelings $$f$$ with the property that $$|v_f(0)-v_f(1)|\leq 1$$. In this paper, we study the product-cordial index sets of Möbius ladders and their bridge join with other cubic graphs. We show that no Möbius ladder is product cordial.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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