Mean labelling of graphs obtained by identifying two graphs. (English) Zbl 1144.05328

Summary: A graph \(G=(V,E)\) with \(p\) vertices and \(q\) edges is said to be a mean graph if it is possible to label the vertices \(x\in V\) with distinct elements \(f(x)\) from \(0,1,2,\dots,q\) in such a way that when each edge \(e=uv\) is labelled with \((f(u)+f(v))/2\) if \(f(u)+f(v)\) is even and \((f(u)+f(v)+1)/2\) if \(f(u)+f(v)\) is odd, then the resulting edge labels are distinct. \(f\) is called a mean labeling of \(G\). In this paper, we investigate the mean labeling of caterpillar, \(C_n^{(2)}\), dragon, arbitrary super subdivision of a path and some graphs which are obtained from cycles and stars.


05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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