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On the edge‐biclique graph and the iterated edge‐biclique operator
Author(s) -
Montero Leandro,
Legay Sylvain
Publication year - 2022
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22775
Subject(s) - complete bipartite graph , mathematics , combinatorics , bipartite graph , iterated function , discrete mathematics , intersection graph , graph , line graph , mathematical analysis
A biclique of a graph G is a maximal induced complete bipartite subgraph of G . The edge‐biclique graph of G , K B e ( G ) , is the edge‐intersection graph of the bicliques of G . A graph G diverges (resp. converges or is periodic) under an operator H whenever lim k → ∞ ∣ V ( H k ( G ) ) ∣ = ∞ (resp. lim k → ∞H k ( G ) = H m ( G ) for some m or H k ( G ) = H k + s( G ) for some k and s ≥ 2 ). The iterated edge‐biclique graph of G , K B e k ( G ) , is the graph obtained by applying the edge‐biclique operator k successive times to G . In this article, we first study the connectivity relation between G and K B e ( G ) . Next, we study the iterated edge‐biclique operator K B e . In particular, we give sufficient conditions for a graph to be convergent or divergent under the operator K B e , we characterize the behavior of burgeon graphs and we propose some general conjectures on the subject.