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On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels. (English) Zbl 1334.05146
Summary: A vertex labeling \(f : V\to \mathbb Z_2\) of a simple graph \(G = (V, E)\) induces two edge labelings \(f^+, f^\ast: E\to \mathbb Z_2\) defined by \(f^+(uv) = f(u) + f(v)\) and \(f^\ast(uv) = f(u)f(v)\). For each \(i\in \mathbb Z_2\), let \(v_f(i) = |\{v\in V : f(v) = i\}|\), \(e^+_f(i) = |\{e\in E : f^+(e) = i\}|\) and \(e^\ast_f(i) = |\{e\in E : f^\ast(e) = i\}|\). We call \(f\) friendly if \(|v_f(0)- v_f(1)|\leq 1\). The friendly index set and the product-cordial index set of \(G\) are defined as the sets \(\{|e^+_f(0)- e^+_f(1)| : \text{}f\) is friendly

MSC:
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
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