Geodesic
Some additions to the theory of star partitions of graphs
Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 119-134.

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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.
Keywords: graph, eigenvalues, eigenspaces, star partitions 
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Bell, Francis; Cvetković, Dragos; Rowlinson, Peter; Simić, Slobodan. Some additions to the theory of star partitions of graphs. Discussiones Mathematicae. Graph Theory, Tome 19 (1999) no. 2, pp. 119-134. http://geodesic.mathdoc.fr/item/DMGT_1999_19_2_a0/

[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.