An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of a graph G was defined by I.Gutman and F. Harary as I(G , x) = Σ =os(G , k)xk , where s(G,k)is the number of independent sets of G of size k and s( G, 0) 1....
Let $G$ be a simple graph of order $n$. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of $G$ is the polynomial $I(G,x)=\sum_{k=0}^{n} s(G,k) x^{k}$, where $s(G,k)$ is the number of independent sets of $G$...
A maximal independent set is an independent set that is not a proper subset of any other independent set. In this paper, we determine the third largest number of maximal independent sets among all graphs of order n⩾3 and identify the corresponding extremal graphs. This is a preview of sub...
Graphs with the second largest number of maximal independent sets ☆Maximal (maximum) independent setExtremal graphLet G be a simple undirected graph. Denote by mi ( G ) (respectively, xi ( G )) the number of maximal (respectively, maximum) independent sets in G. Erds and Moser raised the...
The number of seats in the restaurant is coordinated with the respective trainset configuration and can be flexibly adjusted according to need. The ICE 4 is a true world champion in usable space To provide more seating rows for the same train length as an ICE 3, the seats in the ICE ...
We first propose O (n 2 logn ) time in-place algorithms for finding the maximum clique of the intersection graphs of a set of axis-parallel rectangles of arbitrary sizes. For the rectangle intersection graph of fixed height rectangles, the time complexity can be slightly improved to O (n ...
We are in particular interested in the minimal dispersion of point sets; thus we set disp∗(n,d)=infT⊂[0,1]d,|T|=ndisp(T).It turns out that this minimal dispersion is of asymptotic order 1∕n as a function of n. Consequently, to capture the dependence of this quantity on the...
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performed with a chunk size of 3 Mb with default parameters on the full set of 2186 phased haplotypes (August Molecular Psychiatry (2018), 666 – 673 Genetic overlap in PTSD and SCZ and sex differences in heritability LE Duncan et al 668 2012, 30 069 288 variants, release 'v3.macGT1')...
independent polyploidy events predicted by the 1KP study42; our results here suggest instead a single Pan-Myrtales whole genome duplication (blue rectangle) which followed the gamma hexaploidy (orange triangle) present in all core eudicots.dSynonymous substitution rate density plots for internal polypl...