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1999 | 19 | 2 | 119-134
Tytuł artykułu

Some additions to the theory of star partitions of graphs

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper contains a number of results in the theory of star partitions of graphs. We illustrate a variety of situations which can arise when the Reconstruction Theorem for graphs is used, considering in particular galaxy graphs - these are graphs in which every star set is independent. We discuss a recursive ordering of graphs based on the Reconstruction Theorem, and point out the significance of galaxy graphs in this connection.
Słowa kluczowe
Wydawca
Rocznik
Tom
19
Numer
2
Strony
119-134
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-01-04
poprawiono
1999-08-06
Twórcy
  • Mathematics and Statistics Group, Department of Computing Science and Mathematics, University of Stirling, Scotland FK9 4LA, United Kingdom
  • Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, P.O. Box 35-54, 11120 Belgrade, Yugoslavia
  • Mathematics and Statistics Group, Department of Computing Science and Mathematics, University of Stirling, Scotland FK9 4LA, United Kingdom
  • Department of Mathematics, Faculty of Electrical Engineering, University of Belgrade, P.O. Box 35-54, 11120 Belgrade, Yugoslavia
Bibliografia
  • [1] G. Caporossi, D. Cvetković, P. Hansen, S. Simić, Variable neighborhood search for extremal graphs, 3: on the largest eigenvalue of color-constrained trees, to appear.
  • [2] D. Cvetković, Star partitions and the graph isomorphism problem, Linear and Multilinear Algebra 39 (1995) No. 1-2 109-132.
  • [3] D. Cvetković, M. Doob, H. Sachs, Spectra of Graphs (3rd edition, Johann Ambrosius Barth Verlag, Heidelberg, 1995).
  • [4] D. Cvetković, M. Petrić, A table of connected graphs on six vertices, Discrete Math. 50 (1984) 37-49, doi: 10.1016/0012-365X(84)90033-5.
  • [5] D. Cvetković, P. Rowlinson, S. Simić, Eigenspaces of Graphs (Cambridge University Press, Cambridge, 1997).
  • [6] D. Cvetković, P. Rowlinson, S.K. Simić, Graphs with least eigenvalue -2: the star complement technique, to appear.
  • [7] M. Doob, An inter-relation between line graphs, eigenvalues and matroids, J. Combin. Theory (B) 15 (1973) 40-50, doi: 10.1016/0095-8956(73)90030-0.
  • [8] M.N. Ellingham, Basic subgraphs and graph spectra, Australasian J. Combin. 8 (1993) 247-265.
  • [9] C.D. Godsil, Matching and walks in graphs, J. Graph Theory 5 (1981) 285-297, doi: 10.1002/jgt.3190050310.
  • [10] E.L. Lawler, J.K. Lenstra, A.H.G. Rinnoy Kan, D.B. Schmoys, eds., The traveling salesman problem (John Wiley and Sons, Chichester - New York - Brisbane - Toronto - Singapore, 1985).
  • [11] P. Rowlinson, Dominating sets and eigenvalues of graphs, Bull. London Math. Soc. 26 (1994) 248-254, doi: 10.1112/blms/26.3.248.
  • [12] P. Rowlinson, Star sets and star complements in finite graphs: a spectral construction technique, in: Proc. DIMACS Workshop on Discrete Mathematical Chemistry (March 1998), to appear.
  • [13] P. Rowlinson, On graphs with multiple eigenvalues, Linear Algebra and Appl. 283 (1998) 75-85, doi: 10.1016/S0024-3795(98)10082-4.
  • [14] P. Rowlinson, Linear Algebra, in: eds. L.W. Beineke and R.J. Wilson, Graph Connections (Oxford Lecture Series in Mathematics and its Applications 5, Oxford University Press, Oxford, 1997) 86-99.
  • [15] J.J. Seidel, Eutactic stars, in: eds. A. Hajnal and V.T. Sós, Combinatorics (North-Holland, Amsterdam, 1978) 983-999.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1089
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