Abstract
The concept of [r,s,t]-colourings was introduced by A. Kemnitz and M.Marangio in 2007 as follows: Let G = ( V (G), E(G)) be a graph with vertex set V(G) and E(G). Given non-negative integers r, s and t, an [r,s,t]-colouring of a graph G = ( V (G), E(G)) is a mapping C from V (G) ∪ E(G) to the colour set { 0, 1, 2, ⋯ k –1 } such that |c(v i ) − c(v j )| ≥ r for every two adjacent vertices v i , v j ,| c(e i ) − c(e j )| ≥ s for every two adjacent edges e i , e j , and |c(v i ) − c(e j )| ≥ t for all pairs of incident vertices and edges, respectively. The [r,s,t]-chromatic number χ r, s, t (G) of G is defined to be the minimum k such that G admits an [r,s,t]-colouring. In this paper, we determine the [r,s,t]-chromatic number for join graphs O m + C n .
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Ming-Zhong, M., Yu-Mei, P. (2013). [r, s,t] – Colouring of One Kind of Join Graphs. In: Yang, G. (eds) Proceedings of the 2012 International Conference on Communication, Electronics and Automation Engineering. Advances in Intelligent Systems and Computing, vol 181. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31698-2_93
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DOI: https://doi.org/10.1007/978-3-642-31698-2_93
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