Kong, Man C.; Lee, Sin-Min; Evans, Herbert A.; Kwong, Harris On balance index sets of generalized wheels. (English) Zbl 1234.05199 J. Comb. Math. Comb. Comput. 78, 65-74 (2011). 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.) Keywords:vertex labeling; partial edge labeling; balance index sets; generalized wheels PDF BibTeX XML Cite \textit{M. C. Kong} et al., J. Comb. Math. Comb. Comput. 78, 65--74 (2011; Zbl 1234.05199)