Strong Twins of Ordinary Star-Like Self-Contained Graphs
Mohammad Hadi Shekarriz, Madjid Mirzavaziri
TL;DR
This paper introduces a class of infinite graphs called ordinary star-like self-contained graphs and proves that each such graph either has infinitely many strong twins or none, revealing a dichotomy in their structure.
Contribution
The paper defines ordinary star-like self-contained graphs and establishes a dichotomy regarding the existence of their strong twins.
Findings
Every ordinary star-like self-contained graph has either infinitely many strong twins or none.
The paper introduces a new class of self-contained graphs with specific structural properties.
Abstract
A self-contained graph is an infinite graph which is isomorphic to one of its proper induced subgraphs. In this paper, ordinary star-like self-contained graphs are introduced and it is shown that every ordinary star-like self-contained graph has infinitely many strong twins or none.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Graph Labeling and Dimension Problems