IJPAM: Volume 87, No. 6 (2013)

ACYCLIC EDGE-COLORING OF SIERPINSKI-LIKE GRAPHS

D. Paul$^1$, Indra Rajasingh$^2$
$^{1,2}$School of Advanced Sciences
VIT University
Chennai Campus, INDIA


Abstract. An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number $k$ such that there is an acyclic edge coloring using $k$ colors and is denoted by $\chi_a'(G)$. Sierpinski graphs $S(n,3)$ are the graphs of the Tower of Hanoi with $n$ disks, while Sierpinski gasket graphs $S_n$ are the graphs naturally defined by the finite number of iterations that lead to the Sierpinski gasket. Sierpinski graph and Sierpinski gasket constitute Sierpinski-like graphs. We give algorithms for coloring the Sierpinski-like graphs acyclically using optimal set of colors.

Received: September 6, 2013

AMS Subject Classification: 05C15

Key Words and Phrases: acyclic edge-coloring, acyclic chromatic index, sierpinski graph, sierpinski gasket

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DOI: 10.12732/ijpam.v87i6.14 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 6