On the size of two families of unlabeled bipartite graphs

On the size of two families of unlabeled bipartite graphs

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Let denote the set of unlabeled bipartite graphs whose edges connect a set of vertices with a set of vertices. In this paper, we provide exact formulas for and using Polya’s Counting Theorem. Extending these results to involves solving a set of complex recurrences and remains open. In particular, th...

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Bibliographic Details
Main Authors: Abdullah Atmaca, A. Yavuz Oruç
Format: Article
Language:English
Published: Taylor & Francis Group 2019-08-01
Series:AKCE International Journal of Graphs and Combinatorics
Subjects:
bipartite graph isomorphism
closed-form formula
polya’s counting theorem
unlabeled bipartite graph
Online Access:http://dx.doi.org/10.1016/j.akcej.2017.11.008
Description
Summary:Let denote the set of unlabeled bipartite graphs whose edges connect a set of vertices with a set of vertices. In this paper, we provide exact formulas for and using Polya’s Counting Theorem. Extending these results to involves solving a set of complex recurrences and remains open. In particular, the number of recurrences that must be solved to compute is given by the number of partitions of that is known to increase exponentially with by Ramanujan–Hardy–Rademacher’s asymptotic formula.
ISSN:0972-8600

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