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51.
《Discrete Mathematics》2019,342(10):2846-2849
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In Korchmáros et al. (2018)one-factorizations of the complete graph are constructed for with any odd prime power such that either or . The arithmetic restriction is due to the fact that the vertices of in the construction are the points of a conic in the finite plane of order . Here we work on the Euclidean plane and describe an analogous construction where the role of is taken by a regular -gon. This allows us to remove the above constraints and construct one-factorizations of for every even . 相似文献
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A compact graph-like space is a triple , where is a compact, metrizable space, is a closed zero-dimensional subset, and is an index set such that . New characterizations of compact graph-like spaces are given, connecting them to certain classes of continua, and to standard subspaces of Freudenthal compactifications of locally finite graphs. These are applied to characterize Eulerian graph-like compacta. 相似文献
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《Discrete Mathematics》2022,345(5):112798
This contribution gives an extensive study on spectra of mixed graphs via its Hermitian adjacency matrix of the second kind (N-matrix for short) introduced by Mohar [25]. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from u to v is equal to the sixth root of unity (and its symmetric entry is ); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. The main results of this paper include the following: equivalent conditions for a mixed graph that shares the same spectrum of its N-matrix with its underlying graph are given. A sharp upper bound on the spectral radius is established and the corresponding extremal mixed graphs are identified. Operations which are called two-way and three-way switchings are discussed–they give rise to some cospectral mixed graphs. We extract all the mixed graphs whose rank of its N-matrix is 2 (resp. 3). Furthermore, we show that if is a connected mixed graph with rank 2, then is switching equivalent to each connected mixed graph to which it is cospectral. However, this does not hold for some connected mixed graphs with rank 3. We identify all mixed graphs whose eigenvalues of its N-matrix lie in the range for . 相似文献