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Edge product cordial labeling of some graphs

Prajapati U.M., Patel N.B.

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 1

69--76

For a graph G = (V(G),E(G)) having no isolated vertex, a function ƒ : E(G)→{0;1} is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex be such that the number of edges with label 0 and the number of edges with label 1 differ by at the most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at the most 1. In this paper we discuss the edge product cordial labeling of the graphs Wn(t), PSn and DPSn.

Decomposition of complete graphs into small graphs

Froncek D.

Opuscula Mathematica

2010

Vol. 30, no. 3

277-280

In 1967, A. Rosa proved that if a bipartite graph G with n edges has an α-labeling, then for any positive integer p the complete graph K(2np+1) can be cyclically decomposed into copies of G. This has become a part of graph theory folklore since then. In this note we prove a generalization of this result. We show that every bipartite graph H which decomposes K(k) and K(m) also decomposes K(km).

α2-labeling of graphs

Froncek D.

Opuscula Mathematica

2009

Vol. 29, no. 4

393-397

We show that if a graph G on n edges allows certain special type of rosy labeling (a.k.a. rho;-labeling), called α2-labeling, then for any positive integer k the complete graph K2nk+1 can be decomposed into copies of G. This notion generalizes the α-labeling introduced in 1967 by A. Rosa.