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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.)
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