On Neighbor‐Distinguishing Index of Planar Graphs |
| |
| Authors: | Mirko Horňák Danjun Huang Weifan Wang |
| |
| Affiliation: | 1. INSTITUTE OF MATHEMATICS, P. J. ?AFáRIK UNIVERSITY IN KO?ICE, KO?ICE, SLOVAKIA;2. DEPARTMENT OF MATHEMATICS, ZHEJIANG NORMAL UNIVERSITY, JINHUA, CHINA |
| |
| Abstract: | A proper edge coloring of a graph G without isolated edges is neighbor‐distinguishing if any two adjacent vertices have distinct sets consisting of colors of their incident edges. The neighbor‐distinguishing index of G is the minimum number ndi(G) of colors in a neighbor‐distinguishing edge coloring of G. Zhang, Liu, and Wang in 2002 conjectured that  if G is a connected graph of order at least 6. In this article, the conjecture is verified for planar graphs with maximum degree at least 12. |
| |
| Keywords: | color set neighbor‐distinguishing edge coloring neighbor‐distinguishing index planar graph |
|
|
