Clique irreducibility of some iterative classes of graphs | Zendy

Aparna Lakshmanan S | Zendy; Ambat Vijayakumar | Zendy

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Clique irreducibility of some iterative classes of graphs

Author(s) -

Aparna Lakshmanan S,

Ambat Vijayakumar

Publication year - 2008

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1407

Subject(s) - combinatorics , mathematics , irreducibility , vertex (graph theory) , clique graph , split graph , simplex graph , block graph , discrete mathematics , clique sum , clique number , clique , chordal graph , graph , line graph , 1 planar graph , pure mathematics , graph power

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

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