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%I #12 Jan 04 2019 04:50:52
%S 1,2,8,61,762,13204,300155,8950176
%N Number of labeled star-like graphs on n vertices.
%C Graph G is called star-like if and only if one of its clique trees forms a star.
%C The first seven terms published in the Bina Ph.D. thesis.
%H V. Bina, <a href="https://insis.vse.cz/zp/index.pl?prehled=vyhledavani;podrobnosti_zp=32066;zp=32066;dinfo_jazyk=3">Multidimensional probability distributions: Structure and learning</a>, Ph.D. Thesis. Fac. of Management, University of Economics in Prague (2011)
%o # R code
%o library(igraph)
%o bits <- function(x, n) { # decodes binary representation of graphs
%o list <- NULL
%o while (x > 0) {
%o list <- c(list, x %% 2)
%o x <- x %/% 2
%o }
%o while (length(list) < n) {list <- c(list,0)}
%o return(list)
%o }
%o n<-5 # number of vertices
%o edges <- choose(n,2)
%o models <- 0:(2^edges-1) # all graphs on n vertices
%o mat <- matrix(rep(0,n^2),ncol=n) #adjacency matrix
%o nstar <- 0
%o for (m in models) {
%o mat[lower.tri(mat)] <- bits(m,hran)
%o l <- maximal.cliques(graph.adjacency(mat,mode="lower"))
%o aux <- factor(unlist(l))
%o l <- lapply(l,setdiff, levels(aux)[tabulate(aux) == 1])
%o l <- lapply(l,setdiff,l[[which.max(unlist(lapply(l,length)))]])
%o if (sum(unlist(lapply(l,length))) < 1) nstar <- nstar + 1
%o }
%o nstar
%Y Cf. A179534, A006125, A058862 (sub- and superclasses)
%K nonn
%O 1,2
%A _Vladislav Bina_, Feb 25 2012
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