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

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## 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

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*Graph Theory*(Addison-Wesley Publ. Comp, Massachusetts, Reading, 1969)CrossRefGoogle Scholar - 3.V.R. Kulli, M.H. Muddebihal, The lict graph and litact graph of a graph. J. Anal. Comput.
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