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T-Coloring of Certain Networks

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Abstract

Given a graph G and a finite set T of non-negative integers containing zero, a T-coloring of G is a non-negative integer function f defined on V(G) such that \(|f(x)-f(y)|\not \in T\) whenever \((x,y)\in E(G)\). The span of T-coloring is the difference between the largest and smallest colors, and the T-span of G is the minimum span over all T-colorings f of G. The edge span of a T-coloring is the maximum value of \(|f(x)-f(y)|\) over all edges \((x,y)\in E(G)\), and the T-edge span of G is the minimum edge span over all T-colorings f of G. In this paper, we compute T-span and T-edge span of crown graph, circular ladder and mobius ladder, generalized theta graph, series-parallel graph and wrapped butterfly network.

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Authors and Affiliations

  1. Research and Development Centre, Bharathiar University, Coimbatore, India

    P. Sivagami

  2. Department of Mathematics, Jeppiaar Engineering College, Chennai, India

    P. Sivagami

  3. School of Advanced Sciences, VIT University, Chennai, India

    Indra Rajasingh

Authors
  1. P. Sivagami
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  2. Indra Rajasingh
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Correspondence to P. Sivagami.

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Sivagami, P., Rajasingh, I. T-Coloring of Certain Networks. Math.Comput.Sci. 10, 239–248 (2016). https://doi.org/10.1007/s11786-016-0260-6

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  • DOI: https://doi.org/10.1007/s11786-016-0260-6

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