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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.

REFERENCES

V. Bina, Multidimensional probability distributions: Structure and learning, Ph.D. Thesis. Fac. of Management, University of Economics in Prague (2011).

LINKS

Table of n, a(n) for n=1..8.

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: A191553 A139017 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 February 25 06:31 EST 2018. Contains 299643 sequences. (Running on oeis4.)