,
L. E. Teshima
The independent domination number i(G) of a graph G is the minimum cardinality of a maximal independent set of G, also called an i(G)-set. The i-graph of G, denoted ℐ (G), is the graph whose vertices correspond to the i(G)-sets, and where two i(G)-sets are adjacent if and only if they differ by two adjacent vertices. Not all graphs are i-graph realizable, that is, given a target graph H, there does not necessarily exist a source graph G such that H = ℐ (G). We consider a class of graphs called “theta graphs”: a theta graph is the union of three internally disjoint nontrivial paths with the same two distinct end vertices. We characterize theta graphs that are i-graph realizable, showing that there are only finitely many that are not. We also characterize those line graphs and claw-free graphs that are i-graphs, and show that all 3-connected cubic bipartite planar graphs are i-graphs.
Download files
Citation rules
Licence
This work is licensed under a Creative Commons Attribution 4.0 International License.
The Copyright Holders of the submitted text are the Author and the Journal. The Reader is granted the right to use the pdf documents under the provisions of the Creative Commons 4.0 International License: Attribution (CC BY). The user can copy and redistribute the material in any medium or format and remix, transform, and build upon the material for any purpose.
You may also start an advanced similarity search for this article.
2024
Published: 2024-01-18
10.1515/amsil
English