Maximizing the total number of spanning trees in a graph: Two related problems in graph theory and optimum design theory
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چکیده
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Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1981
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(81)80028-7