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By complexity of a finite graph we mean the number of spanning trees in the graph. The aim of the present paper is to give a new approach for counting complexity $tau(n)$ of cyclic $n$-fold coverings of a graph. We give an explicit analytic formula for $tau(n)$ in terms of Chebyshev polynomials and find its asymptotic behavior as $ntoinfty$ through the Mahler measure of the associated voltage polynomial. We also prove that $F(x)=sumlimits_{n=1}^inftytau(n)x^n$ is a rational function with integer coefficients.
A proper edge coloring of a graph $G$ with colors $1,2,dots,t$ is called a cyclic interval $t$-coloring if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is considered as con
A proper edge coloring of a graph $G$ with colors $1,2,dots,t$ is called a emph{cyclic interval $t$-coloring} if for each vertex $v$ of $G$ the edges incident to $v$ are colored by consecutive colors, under the condition that color $1$ is considered
A proper edge-coloring of a graph $G$ with colors $1,ldots,t$ is called an emph{interval cyclic $t$-coloring} if all colors are used, and the edges incident to each vertex $vin V(G)$ are colored by $d_{G}(v)$ consecutive colors modulo $t$, where $d_{
We determine the maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers and we completely characterize the extremal graphs. As an application, we give a similar result for Konig-Egervary graphs in terms of their matching numbers.
We describe the birational and the biregular theory of cyclic and Abelian coverings between real varieties.