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pro vyhledávání: '"Mednykh, Alexander"'
In this paper, we investigate the complexity of an infinite family of Cayley graphs $\mathcal{D}_{n}=Cay(\mathbb{D}_{n}, b^{\pm\beta_1},b^{\pm\beta_2},\ldots,b^{\pm\beta_s}, a b^{\gamma_1}, a b^{\gamma_2},\ldots, a b^{\gamma_t} )$ on the dihedral gro
Externí odkaz:
http://arxiv.org/abs/2312.16447
In the present paper we compute the Jacobian group of $\Delta$-graph $\Delta(n; k, l, m).$ The notion of $\Delta$-graph continues the list of families of $I$-, $Y$- and $H$-graphs well-known in the graph theory. In particular, graph $\Delta(n; 1, 1,
Externí odkaz:
http://arxiv.org/abs/2211.12007
In the present paper we investigate the faithfulness of certain linear representations of groups of automorphisms of a graph $X$ in the group of symmetries of the Jacobian of $X$. As a consequence we show that if a $3$-edge-connected graph $X$ admits
Externí odkaz:
http://arxiv.org/abs/2206.01469
We present a construction of Neumaier graphs with nexus 1, which generalises two known constructions of Neumaier graphs. We also use W. Wang, L. Qiu, and Y. Hu switching to show that we construct cospectral Neumaier graphs. Finally, we show that seve
Externí odkaz:
http://arxiv.org/abs/2109.13884
The hyperbolic structure on a 3-dimensional cone-manifold with a knot as singularity can often be deformed into a limiting Euclidean structure. In the present paper we show that the respective normalised Euclidean volume is always an algebraic number
Externí odkaz:
http://arxiv.org/abs/2107.03275
We investigate a representation of the automorphism group of a connected graph $X$ in the group of unimodular matrices $U_\beta$ of dimension $\beta$, where $\beta$ is the Betti number of graph $X$. We classify the graphs for which the automorphism g
Externí odkaz:
http://arxiv.org/abs/2102.04239
Publikováno v:
In Discrete Mathematics July 2023 346(7)
In the present paper, we investigate the complexity of infinite family of graphs $H_n=H_n(G_1,\,G_2,\ldots,G_m)$ obtained as a circulant foliation over a graph $H$ on $m$ vertices with fibers $G_{1},\,G_{2},\ldots,G_{m}.$ Each fiber $G_{i}=C_{n}(s_{i
Externí odkaz:
http://arxiv.org/abs/1902.05681
Autor:
Mednykh, Alexander, Mednykh, Ilya
In the present paper, we investigate a family of circulant graphs with non-fixed jumps $$G_n=C_{\beta n}(s_1, \ldots,s_k,\alpha_1n,\ldots,\alpha_\ell n),\, 1\le s_1<\ldots
Externí odkaz:
http://arxiv.org/abs/1812.04484
Autor:
Mednykh, Alexander, Mednykh, Ilya
In this paper, we develop a new method to produce explicit formulas for the number $\tau(n)$ of spanning trees in the undirected circulant graphs $C_{n}(s_1,s_2,\ldots,s_k)$ and $C_{2n}(s_1,s_2,\ldots,s_k,n).$ Also, we prove that in both cases the nu
Externí odkaz:
http://arxiv.org/abs/1711.00175