ON THE EDGE-BALANCE INDEX SETS OF L-PRODUCT OF CYCLES
Abstract: Let G be a simple
graph with vertex set V (G) and edge set E(G), and let Z2 = f0; 1g. 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 i 2 Z2, let vf (i) = v 2 V (G) : f+(v) = i and let ef (i) = jfe 2
E(G) : f(e) = igj. 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, exact values of
the edge-balance index sets of L-product of cycles with cycles, Cn ×L Cm are
presented.
Key words: Edge labeling,
edge-friendly labeling, cordiality, edge-balance index set, L-products, cycles
Author: Daniel Bouchard,
Patrick Clark, and Hsin-Hao Su
Journal Code: jpmatematikagg110026
