A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
The size of switching classes with skew gains
Tekijät: Hage J, Harju T
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2000
Lehti:: Discrete Mathematics
Tietokannassa oleva lehden nimi: DISCRETE MATHEMATICS
Lehden akronyymi: DISCRETE MATH
Vuosikerta: 215
Numero: 1-3
Aloitussivu: 81
Lopetussivu: 92
Sivujen määrä: 12
ISSN: 0012-365X
DOI: https://doi.org/10.1016/S0012-365X(99)00243-5
Tiivistelmä
Gain graphs are graphs in which each edge has a gain (a label from a group, say Gamma, so that reversing the direction inverts the gain). In this paper we take a generalized view of gain graphs in which the gain of an edge is related to the gain of the reverse edge by an anti-involution. These gain graphs will be called skew gain graphs. We define switching by a selector, a generalization of switching (or Seidel switching) of an undirected graph. In this paper we compute the sizes of the resulting equivalence classes of skew gain graphs. This size can be determined by computing the size of an appropriate subgroup of Gamma. We first examine the case that the graph is complete. Then we show how to reduce the general problem to connected graphs and prove that if the graph is connected, but not bipartite, it can be reduced to the complete case. The connected, bipartite case is solved separately. (C) 2000 Elsevier Science B.V. All rights reserved.
Gain graphs are graphs in which each edge has a gain (a label from a group, say Gamma, so that reversing the direction inverts the gain). In this paper we take a generalized view of gain graphs in which the gain of an edge is related to the gain of the reverse edge by an anti-involution. These gain graphs will be called skew gain graphs. We define switching by a selector, a generalization of switching (or Seidel switching) of an undirected graph. In this paper we compute the sizes of the resulting equivalence classes of skew gain graphs. This size can be determined by computing the size of an appropriate subgroup of Gamma. We first examine the case that the graph is complete. Then we show how to reduce the general problem to connected graphs and prove that if the graph is connected, but not bipartite, it can be reduced to the complete case. The connected, bipartite case is solved separately. (C) 2000 Elsevier Science B.V. All rights reserved.
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