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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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