Affiliation:
1. School of Advanced Sciences, Vellore Institute of Technology, Vandalur, Kelambakkam Road, Chennai 600127, India
Abstract
A graph G with acyclic coloring has no two adjacent vertices with the same color and no bichromatic cycle. Also, the coloring results in a forest when any two-color classes are combined. The concept of acyclic coloring plays a pivotal role in the computation of Hessians, Kekule structures classification, coding theory, and statistical mechanics. In this paper, the acyclic chromatic number of generalized fan graph, generalized Möbius ladder graph and flower snark graph have been determined.
Publisher
Fuji Technology Press Ltd.
Subject
Artificial Intelligence,Computer Vision and Pattern Recognition,Human-Computer Interaction
Reference10 articles.
1. B. Grünbaum, “Acyclic colorings of planar graphs,” Israel J. of Mathematics, Vol.14, pp. 390-408, 1973.
2. A. V. Kostochka, “Upper bounds on the chromatic functions of graphs,” Ph.D. Thesis, Novosibirsk, Russia, 1978.
3. A. H. Gebremedhin, A. Tarafdar, F. Manne, and A. Pothen, “New Acyclic and Star Coloring Algorithms with Application to Computing Hessians,” SIAM J. on Scientific Computing, Vol.29, No.3, pp. 1042-1072, 2007.
4. A. T. Balaban, “Applications of graph theory in chemistry,” J. of Chemical Information and Computer Sciences, Vol.25, pp. 334-343, 1985.
5. J. E. Graver and E. J. Hartung, “Kekuléan benzenoids,” J. of Mathematical Chemistry, Vol.52, pp. 977-989, 2014.