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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.)
cordial graphs