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Two‐arc closed subsets of graphs
Author(s) -
Conder Marston,
Morton Margaret,
Praeger Cheryl E.
Publication year - 2003
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.10102
Subject(s) - combinatorics , mathematics , vertex (graph theory) , partition (number theory) , arc (geometry) , discrete mathematics , frequency partition of a graph , graph , line graph , graph power , geometry
A subset of vertices of a graph is said to be 2‐arc closed if it contains every vertex that is adjacent to at least two vertices in the subset. In this paper, 2‐arc closed subsets generated by pairs of vertices at distance at most 2 are studied. Several questions are posed about the structure of such subsets and the relationships between two such subsets, and examples are given from the class of partition graphs. © 2003 Wiley Periodicals, Inc. J Graph Theory 42: 350–364, 2003