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- Title
On the AVSDT-Coloring of S<sub>m</sub> +W<sub>n</sub>.
- Authors
Zhongfu Zhang; Enqiang Zhu; Baogen Xu; Yuhong Zhang; Ji Zhang; Jingwen Li
- Abstract
For any vertex u ε V (G), let TN(u) = {u} ∪ {uv∣uv ε E(G), v ε V (G)} ∪ {v ε V (G)∣uv ε E(G)} and f a total k-coloring on G. The total-color neighbor of a vertex u of G is the color set Cf (x) = {f(x)∣x ε TN(u)}. For any adjacent vertices x and y of V (G) such that Cf (x) ≠ Cf (y), we refer to f as a k AVSDT-coloring of G (the abbreviation of adjacent-vertex-strongly-distinguishing total coloring of G). The AVSDT-coloring number of G, denoted by Xast(G) is the minimal number of colors required for an AVSDT-coloring of G. A Smarandachely total coloring of a graph G is an AVSDT-coloring with ∣Cf (x)\Cf (y)∣ ≥ 2 and ∣Cf (y)\Cf (x)∣ ≥ 2. In this paper, we calculate the AVSDT-coloring number of Sm+Wn.
- Subjects
GRAPH coloring; GRAPH theory; GRAPHIC methods; FOUR-color theorem; COMBINATORICS; SMARANDACHE function; SMARANDACHE notions
- Publication
International Journal of Mathematical Combinatorics, 2008, Vol 3, p105
- ISSN
1937-1055
- Publication type
Article