# AVDTC numbers of generalized Halin graphs with maximum degree at least 6

AVDTC numbers of generalized Halin graphs with maximum degree at least 6 In a paper by Zhang and Chen et al.(see ), a conjecture was made concerning the minimum number of colors χ at (G) required in a proper total-coloring of G so that any two adjacent vertices have different color sets, where the color set of a vertex ν is the set composed of the color of ν and the colors incident to ν. We find the exact values of χ at (G) and thus verify the conjecture when G is a Generalized Halin graph with maximum degree at least 6. A generalized Halin graph is a 2-connected plane graph G such that removing all the edges of the boundary of the exterior face of G (the degrees of the vertices in the boundary of exterior face of G are all three) gives a tree. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# AVDTC numbers of generalized Halin graphs with maximum degree at least 6

, Volume 24 (1) – Mar 13, 2008
4 pages      /lp/springer-journals/avdtc-numbers-of-generalized-halin-graphs-with-maximum-degree-at-least-1O9n0O132C
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-005-5222-8
Publisher site
See Article on Publisher Site

### Abstract

In a paper by Zhang and Chen et al.(see ), a conjecture was made concerning the minimum number of colors χ at (G) required in a proper total-coloring of G so that any two adjacent vertices have different color sets, where the color set of a vertex ν is the set composed of the color of ν and the colors incident to ν. We find the exact values of χ at (G) and thus verify the conjecture when G is a Generalized Halin graph with maximum degree at least 6. A generalized Halin graph is a 2-connected plane graph G such that removing all the edges of the boundary of the exterior face of G (the degrees of the vertices in the boundary of exterior face of G are all three) gives a tree.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 13, 2008

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