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A CHARACTERIZATION ON THE ADJACENT VERTEX DISTINGUISHING INDEX OF PLANAR GRAPHS WITH LARGE MAXIMUM DEGREE.
- Source :
-
SIAM Journal on Discrete Mathematics . 2015, Vol. 29 Issue 4, p2412-2431. 20p. 2 Diagrams, 1 Chart. - Publication Year :
- 2015
-
Abstract
- An adjacent vertex distinguishing coloring of a graph G is a proper edge coloring of G such that any pair of adjacent vertices admits different sets of colors. The minimum number of colors needed for such a coloring of G is denoted by χ'a(G). In this paper, we show that if G is a planar graph with maximum degree Δ ≥ 16, then Δ ≤ χ'a(G) ≤ Δ + 1, and χ'a(G) = Δ+1 if and only if G contains two adjacent vertices of maximum degree. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GEOMETRIC vertices
*PLANAR graphs
*GRAPH theory
*SUBSET selection
*GRAPH coloring
Subjects
Details
- Language :
- English
- ISSN :
- 08954801
- Volume :
- 29
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 117002431
- Full Text :
- https://doi.org/10.1137/120903178