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On balance index sets of generalized wheels. (English) Zbl 1234.05199
Summary: A vertex labeling $$f: V\to\{0,1\}$$ of the simple graph $$G= (V,E)$$ induces a partial edge labeling $$f^*: E\to\{0,1\}$$ defined by $$f^*(uv)= f(u)$$ if and only if $$f(u)= f(v)$$. Let $$v(i)$$ and $$e(i)$$ be the number of vertices and edges, respectively, that are labeled $$i$$, and define the balance index set of $$G$$ as $$\{|e(0)- e(1)|:|v(0)- v(1)|\leq 1\}$$.
We determine the balance index sets of generalized wheels, which are the Zykov sum of a cycle with a null graph.
MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.)