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 A208356 Number of labeled star-like graphs on n vertices. 0
 1, 2, 8, 61, 762, 13204, 300155, 8950176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Graph G is called star-like if and only if one of its clique trees forms a star. The first seven terms published in the Bina Ph.D. thesis. LINKS V. Bina, Multidimensional probability distributions: Structure and learning, Ph.D. Thesis. Fac. of Management, University of Economics in Prague (2011) PROG # R code library(igraph) bits <- function(x, n) { # decodes binary representation of graphs   list <- NULL   while (x > 0) {      list <- c(list, x %% 2)      x <- x %/% 2   }   while (length(list) < n) {list <- c(list, 0)}   return(list) } n<-5 # number of vertices edges <- choose(n, 2) models <- 0:(2^edges-1) # all graphs on n vertices mat <- matrix(rep(0, n^2), ncol=n) #adjacency matrix nstar <- 0 for (m in models) {     mat[lower.tri(mat)] <- bits(m, hran)     l <- maximal.cliques(graph.adjacency(mat, mode="lower"))     aux <- factor(unlist(l))     l <- lapply(l, setdiff, levels(aux)[tabulate(aux) == 1])     l <- lapply(l, setdiff, l[[which.max(unlist(lapply(l, length)))]])     if (sum(unlist(lapply(l, length))) < 1) nstar <- nstar + 1 } nstar CROSSREFS Cf. A179534, A006125, A058862 (sub- and superclasses) Sequence in context: A139017 A322012 A188324 * A188489 A085657 A005215 Adjacent sequences:  A208353 A208354 A208355 * A208357 A208358 A208359 KEYWORD nonn AUTHOR Vladislav Bina, Feb 25 2012 STATUS approved

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Last modified January 21 08:28 EST 2019. Contains 319351 sequences. (Running on oeis4.)