Enumeration of connected invariant graphs
نویسندگان
چکیده
منابع مشابه
Asymptotic enumeration of sparse 2-connected graphs
We determine an asymptotic formula for the number of labelled 2-connected (simple) graphs on n vertices and m edges, provided that m−n→∞ and m = O(n logn) as n→∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2-edge-connectedness is treated similarly. We...
متن کاملStructure and enumeration of two-connected graphs with prescribed three-connected components
We adapt the classical 3-decomposition of any 2-connected graph to the case of simple graphs (no loops or multiple edges). By analogy with the block-cutpoint tree of a connected graph, we deduce from this decomposition a bicolored tree tc(g) associated with any 2-connected graph g, whose white vertices are the 3-components of g (3-connected components or polygons) and black vertices are bonds a...
متن کاملEnumeration of the degree sequences of non-separable graphs and connected graphs
In 1962, S. L. Hakimi proved necessary and sufficient conditions for a given sequence of positive integers d1, d2, . . . , dn to be the degree sequence of a non–separable graph or that of a connected graph. Our goal in this note is to utilize these results to prove closed formulas for the functions dns(2m) and dc(2m), the number of degree sequences with degree sum 2m representable by non–separa...
متن کاملEnumeration of Connected Uniform Hypergraphs
In this paper, we are concerned in counting exactly and asymptotically connected labeled b-uniform hypergraphs (b ≥ 3). Enumerative results on connected graphs are generalized here to connected uniform hypergraphs. For this purpose, these structures are counted according to the number of vertices and hyperedges. First, we show how to compute step by step the associated exponential generating fu...
متن کاملEnumeration of cospectral graphs
We have enumerated all graphs on at most 11 vertices and determined their spectra with respect to various matrices, such as the adjacency matrix and the Laplacian matrix. We have also counted the numbers for which there is at least one other graph with the same spectrum (a cospectral mate). In addition we consider a construction for pairs of cospectral graphs due to Godsil and McKay, which we c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1983
ISSN: 0095-8956
DOI: 10.1016/0095-8956(83)90040-0