Clique irreducibility of some iterative classes of graphs

• Autorzy: Aparna Lakshmanan S. , A. Vijayakumar
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

line graphs; Gallai graphs; anti-Gallai graphs; clique irreducible graphs; clique vertex irreducible graphs

Kategorie tematyczne

• 05C99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 2
• Strony: 307-321

Daty

wydano

2008

otrzymano

2007-10-09

poprawiono

2008-03-18

zaakceptowano

2008-03-18

Twórcy

autor

Aparna Lakshmanan S.

• Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India

autor

A. Vijayakumar

• Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India

Bibliografia

• [1] Aparna Lakshmanan S., S.B. Rao and A. Vijayakumar, Gallai and anti-Gallai graphs of a graph, Math. Bohem. 132 (2007) 43-54.
• [2] R. Balakrishnan and K. Ranganathan, A Text Book of Graph Theory (Springer, 1999).
• [3] L. Chong-Keang and P. Yee-Hock, On graphs without multicliqual edges, J. Graph Theory 5 (1981) 443-451, doi: 10.1002/jgt.3190050416.
• [4] V.B. Le, Gallai graphs and anti-Gallai graphs, Discrete Math. 159 (1996) 179-189, doi: 10.1016/0012-365X(95)00109-A.
• [5] E. Prisner, Graph Dynamics (Longman, 1995).
• [6] E. Prisner, Hereditary clique-Helly graphs, J. Combin. Math. Combin. Comput. 14 (1993) 216-220.
• [7] W.D. Wallis and G.H. Zhang, On maximal clique irreducible graphs, J. Combin. Math. Combin. Comput. 8 (1990) 187-193.

Identyfikatory

DOI

10.7151/dmgt.1407