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2008 | 28 | 2 | 307-321
Tytuł artykułu

Clique irreducibility of some iterative classes of graphs

Treść / Zawartość
Warianty tytułu
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.
Wydawca
Rocznik
Tom
28
Numer
2
Strony
307-321
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-10-09
poprawiono
2008-03-18
zaakceptowano
2008-03-18
Twórcy
  • Department of Mathematics, Cochin University of Science and Technology, Cochin-682 022, India
  • 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1407
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