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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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