Contents

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On Edge-Balance Index Sets of L-product of Cycles with Stars, Part I

Chao-Chih Chou1, Meghan Galiardi2, Man Kong3, Sin-Min Lee4, Daniel Perry2
1General Education Center St. John’s University Tamsui, Taipei Shien, Taiwan
2Department of Mathematics Stonehill College Easton, MA 02357, USA
3Department of Electrical Engineering and Computer Science University of Kansas Laurence, KS 66045, USA
4Department of Computer Science San Jose State University San Jose, CA 95192, USA

Abstract

Let G be a simple graph with vertex set V(G) and edge set E(G), and let Z2={0,1}. Any edge labeling f induces a partial vertex labeling f+:V(G)Z2 assigning 0 or 1 to f+(v), v being an element of V(G), depending on whether there are more 0-edges or 1-edges incident with v, and no label is given to f+(v) otherwise. For each iZ2, let vf(i)=|{vV(G):f+(v)=i}| and let ef(i)=|{eE(G):f(e)=i}|. An edge-labeling f of G is said to be edge-friendly if |ef(0)ef(1)|1. The edge-balance index set of the graph G is defined as EBI(G)={|vf(0)vf(1)|:f is edge-friendly}. In this paper, we investigate and present results concerning the edge-balance index sets of L-products of cycles with stars.

Keywords: vertex labeling, edge labeling, friendly labeling, cordiality, edge-balance index set, L-products, cycles, stars.