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pro vyhledávání: '"Mednykh, Ilya"'
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 this paper, we present a new method to produce explicit formulas for the number of rooted spanning forests $f(n)$ for the 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
Externí odkaz:
http://arxiv.org/abs/2111.04297
Autor:
Mednykh, Ilya
The structure of the first homology group of a cyclic covering of a knot is an important invariant well known in the knot theory. In the last century, H. Seifert developed a general approach to compute the homology group of the covering. Based on his
Externí odkaz:
http://arxiv.org/abs/2111.04292
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
Autor:
Mednykh, Ilya
We consider a family of I-graphs I(n,k,l), which is a generalization of the class of generalized Petersen graphs. In the present paper, we provide a new method for counting Jacobian group of the I-graph I(n,k,l). We show that the minimum number of ge
Externí odkaz:
http://arxiv.org/abs/1703.07058
Publikováno v:
Tohoku Mathematical Journal. 74
In this paper, we present a new method to produce explicit formulas for the number of rooted spanning forests $f(n)$ for the 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
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