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The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph $G$ with vertex set $V = {v_{1}, v_{2}, \dots, v_{n}}$ , the extended double cover of $G$ , denoted $G^{*}$ , is the bipartite graph with bipartition $(X, Y)$ where $X = {x_{1}, x_{2}, \dots, x_{n}}$ and $Y = {y_{1}, y_{2}, \dots, y_{n}}$ , in which $x_{i}$ and $y_{j}$ are adjacent iff $i = j$ or $v_{i}$ and $v_{j}$ are adjacent in $G$ . In this paper we obtain formulas for the characteristic polynomial and the spectrum of $G^{*}$ in terms of the corresponding information of $G$ . Three formulas are derived for the number of spanning trees in $G^{*}$ for a connected...

Streng parametrische Bedingungen und die Anzahl ihrer nicht isomorphen Modelle.

D. Wille (1977)

Monatshefte für Mathematik

Structures ofW(2.2) Lie conformal algebra

Lamei Yuan, Henan Wu (2016)

Open Mathematics

The purpose of this paper is to study W(2, 2) Lie conformal algebra, which has a free ℂ[∂]-basis L, M such that [...] [LλL]=(∂+2λ)L,[LλM]=(∂+2λ)M,[MλM]=0 . In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.

Subdeterminants and subgraphs

Antonín Vrba (1974)

Časopis pro pěstování matematiky

Tessellations of random maps of arbitrary genus

Grégory Miermont (2009)

Annales scientifiques de l'École Normale Supérieure

We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing one to encode such structures by labeled maps with a fixed number of faces. We investigate the scaling limits of the latter. Applications include asymptotic enumeration results for quadrangulations, and typical metric properties of randomly sampled quadrangulations. In particular, we show that scaling limits of these...