On the structure of compact graphs

• Autorzy: Nikandish R. , Shaveisi F.

Identyfikatory

DOI

10.7494/OpMath.2017.37.6.875

• Języki publikacji: EN

Abstrakty

EN

A simple graph G is called a compact graph if G contains no isolated vertices and for each pair x, y of non-adjacent vertices of G, there is a vertex z with N(x) ∪ N(y) ⊆ N(z), where N(v) is the neighborhood of v, for every vertex v of G. In this paper, compact graphs with sufficient number of edges are studied. Also, it is proved that every regular compact graph is strongly regular. Some results about cycles in compact graphs are proved, too. Among other results, it is proved that if the ascending chain condition holds for the set of neighbors of a compact graph G, then the descending chain condition holds for the set of neighbors of G.

Słowa kluczowe

EN

compact graph; vertex degree; cycle; neighborhood

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2017
• Tom: Vol. 37, no. 6
• Strony: 875--886
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Nikandish R.

• Department of Basic Sciences Jundi-Shapur University of Technology P.O. Box 64615-334, Dezful, Iran Farzad Shaveisi [e-mail]

autor

Shaveisi F.

• Department of Mathematics Faculty of Sciences Razi University P.O. Box 67149-67346, Kermanshah, Iran

Bibliografia

• [1] G. Aalipour, S. Akbari, R. Nikandish, M.J. Nikmehr, F. Shaveisi, On t/ie coloring of the annihilating-ideal graph of a commutative ring, Discrete. Math. 312 (2012), 2620-2626.
• [2] L.W. Beineke, B.J. Wilson, Selected Topics in Graph Theory, Academic Press Inc., London, 1978.
• [3] J.A. Bondy, U.S.R. Murty, Graph Theory, Graduate Texts in Mathematics, vol. 244, Springer, New York, 2008.
• [4] C. Godsil, G. Royle, Algebraic Graph Theory, New York, Springer-Verlag, 2001.
• [5] R. Halas, M. Jukl, On Beck's coloring of posets, Discrete Math. 309 (2009), 4584-4589.
• [6] R. Halas, H. Langer, The zero-divisor graph of a qoset, Order 27 (2010), 343-351.
• [7] D.C. Lu, T.S. Wu, The zero- divisor zraphs of po sets and an application to semigroups, Graphs and Combin. 26 (2010), 793-804.
• [8] T.S. Wu, D.C. Lu, Sub-semigroups of determined by the zero-divisor graph, Discrete Math. 308 (2008), 5122-5135.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).