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

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


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.


Line graph Lict graph Litact graph Clique Clique chromatic number 


Primary: 05C75 Secondary: 05C76 


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© 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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