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On Cliques and Clique Chromatic Numbers in Line, Lict and Lictact Graphs

  • Rashmi JainEmail author
  • Anuj Kumar Jain
Conference paper
  • 48 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 307)

Abstract

The line graph of a graph G denoted as L(G) has vertex set E(G) in which two vertices are adjacent if they correspond to adjacent edges in G. The lict graph and litact graph of G, denoted as \(L_c(G)\) and \(L_{ct}(G)\), respectively having vertex set \(E(G)\cup C(G)\) (here C(G) is the set of cut-vertices of G), two of these vertices will be adjacent in \(L_c(G)\) if they correspond to adjacent edges of G or one vertex is an edge e of G and other vertex is a cut-vertex c of G such that e is incident to c; and two vertices in \(L_{ct}(G)\) be adjacent if they are adjacent or incident elements of G. In this paper, we establish results on cliques and clique chromatic numbers in line, lict and litact graphs of any graph.

Keywords

Line graph Lict graph Litact graph Clique Clique chromatic number 

MSC(2010):

Primary: 05C75 Secondary: 05C76 

References

  1. 1.
    M. Acharya, R. Jain, S. Kansal, Characterization of line-cut graphs. Graph Theory Notes of New York, LXV, vol. I (2014), pp. 43–46Google Scholar
  2. 2.
    F. Harary, Graph Theory (Addison-Wesley Publ. Comp, Massachusetts, Reading, 1969)CrossRefGoogle Scholar
  3. 3.
    V.R. Kulli, M.H. Muddebihal, The lict graph and litact graph of a graph. J. Anal. Comput. 2(1), 33–43 (2006)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Applied SciencesKIET Group of InstitutionsGhaziabadIndia
  2. 2.Department of Mechanical EngineeringABES Engineering CollegeGhaziabadIndia

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