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Graphs with unique maximal clumpings
Author(s) -
Blass Andreas
Publication year - 1978
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.3190020104
Subject(s) - mathematics , combinatorics , adjacency list , partition (number theory) , frequency partition of a graph , graph , discrete mathematics , wheel graph , graph power , line graph
A partition of the vertices of a graph is called a clumping if, for vertices in distinct partition classes, adjacency depends only on the partition classes, not on the specific vertices. We give a simple necessary and sufficient condition for a finite graph to have a unique maximal clumping. We also investigate the extent to which this and related results generalize to infinite graphs.