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Solving of Chromatic Number, Chromatic Polynomial and Chromaticity for a Kind of 6-Bridge Graph Using Maplesoft | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 58, Issue 4, 2018, Pages 1955-1962 | ||
| Author | ||
| Zeyad Tareq Habeeb | ||
| Abstract | ||
| Maplesoft is a technical computation forms which is a heart of problem solving in mathematics especially in graph theory. Maplesoft has established itself as the computer algebra system for researchers. Maplesoft has more mathematical algorithms which is covering a wide range of applications. A new family θ(3,3,3,4,5,5) of 6-bridge graph still not completely solved for chromatic number, chromatic polynomial and chromaticity. In this paper we apply maplesoft on a kind of 6-bridge graph (G) to obtain chromatic number, chromatic polynomial and chromaticity. The computations are shown that graph G contents 3 different colours for all vertices, 112410 different ways to colour a graph such that any two adjacent vertices have different colour by using 3 different colour, graph G has isomorphic graph which has same chromatic polynomial of graph G. The odd number of vertices located in one of these bridges made chromatic number 3. The chromatic number was the important factor that made the number of way 112410. A bijection function α created isomorphic graph H to graph G and the chromatic polynomial of H was P(H,λ)=P(G,λ). | ||
| Keywords | ||
| chromatic number; Chromatic Polynomial; Chromaticity; Bridge Graph; Maplesoft | ||
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