The composition of graphs

Sabidussi, Gert

doi:10.1215/s0012-7094-59-02667-5

Cited by 123 publications

(53 citation statements)

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“…For the terminology and notation to be used throughout this paper we refer the reader to [8] section 2. In addition we need the following definitions.…”

Section: Introduction Preliminariesmentioning

confidence: 99%

Vertex-transitive graphs

Sabidussi¹

1964

Monatshefte f�r Mathematik

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295

172

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“…For the terminology and notation to be used throughout this paper we refer the reader to [8] section 2. In addition we need the following definitions.…”

Section: Introduction Preliminariesmentioning

confidence: 99%

Vertex-transitive graphs

Sabidussi¹

1964

Monatshefte f�r Mathematik

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295

172

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“…In [12], Sabidussi gives necessary and sufficient conditions for Aut( 1 ) V ( 2 ) Aut( 2 ) = Aut( 1 [ 2 ]), in which case this lower bound becomes equality. His work is generalized in [10] and extended to color digraphs in [8].…”

Section: Springermentioning

confidence: 99%

The distinguishing number of the direct product and wreath product action

Chan

2006

J Algebr Comb

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Let G be a group acting faithfully on a set X . The distinguishing number of the action of G on X , denoted D G (X ), is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a colorpreserving permutation of X . In this paper, we consider the distinguishing number of two important product actions, the wreath product and the direct product. Given groups G and H acting on sets X and Y respectively, we characterize the distinguishing number of the wreath product G Y H in terms of the number of distinguishing colorings of X with respect to G and the distinguishing number of the action of H on Y . We also prove a recursive formula for the distinguishing number of the action of the Cartesian product of two symmetric groups S m × S n on [m] × [n].

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“…Defining the vertices of the resulting graph as ordered pairs of vertices of the component graphs (as in [Har,Sab1,Sab2,Sab3]) turns out to be technically very convenient for the purposes of this paper (see, in particular, the statements of Theorem 4 and Theorem 12).…”

Section: Graphs Clans and Substitutionmentioning

confidence: 99%

Finite Languages for the Representation of Finite Graphs

Ehrenfeucht

Engelfriet

Rozenberg

1996

Journal of Computer and System Sciences

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We introduce a new way of specifying graphs: through languages, i.e., sets of strings. The strings of a given (finite, prefix-free) language represent the vertices of the graph; whether or not there is an edge between the vertices represented by two strings is determined by the pair of symbols at the first position in these strings where they differ. With this new,``positional'' or lexicographic, method, classical and well-understood ways of specifying languages can now be used to specify graphs, in a compact way; thus, (small) finite automata can be used to specify (large) graphs. Since (prefix-free) languages can be viewed as trees, our method generalizes the hierarchical specification of particular types of graphs such as cographs and VSP graphs. Our main results demonstrate an intrinsic relationship between the fundamental operations of language concatenation and graph substitution. ]

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The composition of graphs

Cited by 123 publications

References 0 publications

Vertex-transitive graphs

Vertex-transitive graphs

The distinguishing number of the direct product and wreath product action

Finite Languages for the Representation of Finite Graphs

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