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On friendly index sets and product-cordial index sets of subdivided Möbius ladders. (English) Zbl 1365.05257
Summary: Let \(G\) be a simple graph, and let \(\mathbb{Z}_2\) be the field with two elements. Any vertex labeling \(f: V(G)\to\mathbb{Z}_2\) induces an edge labeling \(f^+: E(G)\to\mathbb{Z}_2\) defined by \(f^+(uv)= f(u)+ f(v)\) for each edge \(uv\in E(G)\). For each \(i\in\mathbb{Z}_2\), define \(v_f(i)=|f^{-1}|\), and \(e_f^+=|(ff^+)^{-1}(i)|\). The friendly index set of a graph \(G\) is defined as the set of possible values of \(|e^+_f (1)- e^+_f(0)|\) taken over all vertex labelings \(f\) with the property that \(|v_f(1)- v_f(0)|\leq 1\).
The corresponding multiplicative version is called the product-cordial index set. In this paper, we determine the friendly index sets and the product-cordial index sets of subdivided Möbius ladders.
MSC:
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Keywords:
cordial graphs
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