Recursively constructible families of graphs
By M. Noy, Ares Ribó Mor. 2004
38 citations recorded by the source corpus.
An infinite sequence of graphs {G"n}"n">="0 is called recursive if the Tutte polynomials T(G"n;x,y) satisfy a linear recurrence relation whose coefficients are polynomials in x and y. In this paper we introduce a general method based on transfer matrices for proving that a family is recursive that covers all examples known to us. As an application we show that, for fixed s, the sequence of complete bipartite graphs {K"s","n} is recursive and satisfies a linear recurrence whose degree is the number of partitions of the integer s.
Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology
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In Computational Theory and Mathematics
In Electrical and Electronic Engineering
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Citations in the corpus
- GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models (2018, background): “For example, suppose that the training set consists of ladder graphs (Noy & Rib´o, 2004).”
- GraphRNN: A Deep Generative Model for Graphs (2018, background): “For example, suppose that the training set consists of ladder graphs (Noy & Ribó, 2004).”
- Betweenness Centrality in Some Classes of Graphs (2014, background): “The ladder graph L n [19, 20] is defined as the Cartesian product 1 2 3 4 5”