Clique irreducibility and clique vertex irreducibility of graphs | Zendy

Aparna Lakshmanan S | Zendy; A. Vijayakumar | Zendy

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Clique irreducibility and clique vertex irreducibility of graphs

Author(s) -

Aparna Lakshmanan S,

A. Vijayakumar

Publication year - 2009

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm0901137l

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

A graphs 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 is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if Gc has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized

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