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## Discussiones Mathematicae Graph Theory

2010 | 30 | 3 | 365-375
Tytuł artykułu

### The edge C₄ graph of some graph classes

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The edge C₄ graph of a graph G, E₄(G) is a graph whose vertices are the edges of G and two vertices in E₄(G) are adjacent if the corresponding edges in G are either incident or are opposite edges of some C₄. In this paper, we show that there exist infinitely many pairs of non isomorphic graphs whose edge C₄ graphs are isomorphic. We study the relationship between the diameter, radius and domination number of G and those of E₄(G). It is shown that for any graph G without isolated vertices, there exists a super graph H such that C(H) = G and C(E₄(H)) = E₄(G). Also we give forbidden subgraph characterizations for E₄(G) being a threshold graph, block graph, geodetic graph and weakly geodetic graph.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
365-375
Opis fizyczny
Daty
wydano
2010
otrzymano
2008-09-05
poprawiono
2009-03-26
zaakceptowano
2009-07-16
Twórcy
autor
• Department of Mathematics, Cochin University of Science and Technology, Cochin-682022, India
autor
• Department of Mathematics, Cochin University of Science and Technology, Cochin-682022, India
Bibliografia
• [1] A. Brandstädt, V.B. Le and J.P. Spinrad, Graph Classes (SIAM, 1999).
• [2] V. Chvátal and P.L. Hammer, Aggregation of inequalities in integer programming, Ann. Discrete Math. 1 (1997) 145-162.
• [3] D.G. Corneil, Y. Perl and I.K. Stewart, A linear recognition algorithm for cographs, SIAM J. Comput. 14 (1985) 926-934, doi: 10.1137/0214065.
• [4] S. Foldes and P.L. Hammer, The Dilworth number of a graph, Ann. Discrete Math. 2 (1978) 211-219, doi: 10.1016/S0167-5060(08)70334-0.
• [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1988).
• [6] E. Howorka, On metric properties of certain clique graphs, J. Combin. Theory (B) 27 (1979) 67-74, doi: 10.1016/0095-8956(79)90069-8.
• [7] D.C. Kay and G. Chartrand, A characterization of certain Ptolemic graphs, Canad. J. Math. 17 (1965) 342-346, doi: 10.4153/CJM-1965-034-0.
• [8] M. Knor, L. Niepel and L. Soltes, Centers in line graphs, Math. Slovaca 43 (1993) 11-20.
• [9] M.K. Menon and A. Vijayakumar, The edge C₄ graph of a graph, in: Proc. International Conference on Discrete Math. Ramanujan Math. Soc. Lect. Notes Ser. 7 (2008) 245-248.
• [10] O. Ore, Theory of Graphs, Amer. Math. Soc. Coll. Publ. 38, (Providence R.I, 1962).
• [11] E. Prisner, Graph Dynamics (Longman, 1995).
• [12] S.B. Rao, A. Lakshmanan and A. Vijayakumar, Cographic and global cographic domination number of a graph, Ars Combin. (to appear).
• [13] D.B. West, Introduction to Graph Theory (Prentice Hall of India, 2003).
Typ dokumentu
Bibliografia
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