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1.
A directed balanced incomplete block design (or D
B(k,;v)) (X,) is called self-converse if there is an isomorphic mapping f from (X,) to (X,–1), where –1={B
–1:B} and B
–1=(x
k
,x
k
–1,,x
2,x
1) for B=(x
1,x
2,,x
k
–1,x
k
). In this paper, we give the existence spectrum for self-converse D
B(4,1;v).
AMS Classification:05BResearch supported in part by NSFC Grant 10071002 and SRFDP under No. 20010004001 相似文献
2.
《Discrete Mathematics》2022,345(10):112989
A mixed graph is cospectral to its converse, with respect to the usual adjacency matrices. Hence, it is easy to see that a mixed graph whose eigenvalues occur uniquely, up to isomorphism, must be isomorphic to its converse. It is therefore natural to ask whether or not this is a common phenomenon. This note contains the theoretical evidence to confirm that the fraction of self-converse mixed graphs tends to zero. 相似文献
3.
《Discrete Mathematics》2022,345(8):112918
Characterizing graphs by the spectra of various matrices associated with the graphs has long been an important topic in spectral graph theory. However, it is generally very hard to show a given graph to be determined by its spectrum. This paper gives a simple criterion for a tournament to be determined by its adjacency spectrum. More precisely, let G be a tournament of order n with adjacency matrix A, and be its walk matrix, where e is the all-one vector. We show that, for any self-converse tournament G, if is square-free, then G is uniquely determined by its adjacency spectrum among all tournaments. The result is somewhat unexpected, which was achieved by employing some recent tools developed by the second author for showing a graph to be determined by its generalized spectrum. The key observation is that for a tournament G, the complement of G coincides with the converse of G, and hence a certain equivalence between the ordinary adjacency spectrum and the generalized (skew)-adjacency spectrum for G can be established. Moreover, some equivalent formulations of the above result, as well as some related ones are also presented. 相似文献
4.
《Discrete Mathematics》2021,344(12):112619
An is a collection of disjoint pure Mendelsohn triple system on the same set of v elements. An is a special which contains exactly converse pairs of . In this paper, we mainly discuss the existence of an for and get the following conclusions: (1) there exists an if and only if and . (2) There exists an with index if and only if . 相似文献
5.
《Discrete Mathematics》2022,345(10):112969
An is a collection of pairwise disjoint on the same set of v elements. An is a special which contains exactly converse hexads of . In this paper, we mainly discuss the existence of an and get the following conclusions: (1) there exists an if and only if except possibly . (2) There exists an with index if and only if except possibly . 相似文献
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