# IJPAM: Volume 41, No. 6 (2007)

**ADJACENT VERTEX DISTINGUISHING TOTAL**

COLORING OF AND DOUBLE GRAPH

COLORING OF AND DOUBLE GRAPH

School of Mathematics, Physics and Software Engineering

Lanzhou Jiaotong University

Lanzhou, 730070, P.R CHINA

e-mail: zhangting1389@126.com

Department of Mathematics

East China Jiaotong University

Jiaotong, P.R. CHINA

**Abstract.**A total coloring is called adjacent vertex distinguishing if every two adjacent vertices are incident to different sets of colored vertex and incident edge with vertex. The minimum number of colors required for a adjacent vertex distinguishing proper total coloring, a simple graph is denoted by .

Let be a simple graph. If
,
and
, then we call is the double graph of graph,where is the copy of .
The paper studies the adjacent vetex distinguishing total chromatic
number of of .

**Received: **May 28, 2007

**AMS Subject Classification: **05C15, 68R10, 94C15

**Key Words and Phrases: **double graph, Adjacent vetex distinguishing total coloring, adjacent vetex distinguishing total chromatic number

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2007

**Volume:** 41

**Issue:** 6