×

A novel labeling algorithm on several classes of graphs. (English) Zbl 1381.05064

Summary: A positive integer \(n\) is called super totient if the residues of \(n\) which are prime to \(n\) can be partitioned into two disjoint subsets of equal sums. Let \(G\) be a given graph with \(V\), the set of vertices and \(E\) is the set of its edges. An injective function \(g\) defined on \(V\) into subset of integers will be termed as super totient labeling of the graph \(G\), if the function \(g^\ast\colon E\to \mathbb{N}\) defined by \(g^\ast(xy)=g(x)g(y)\) assigns a super totient number for all edges \(xy\in E\), where \(x,y\in V\). A graph admits this labeling is called a super totient graph. In the current manuscript, the authors investigate a novel labeling algorithm, called super totient labeling, for several classes of graphs such as friendship graphs, wheel graphs, complete graphs and complete bipartite graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C85 Graph algorithms (graph-theoretic aspects)
11A25 Arithmetic functions; related numbers; inversion formulas
PDFBibTeX XMLCite
Full Text: Link