Transitivity on Minimum Dominating Sets of Paths and Cycles

Autor:	Gerardo Reyna-Hérnandez, Jesús Romero-Valencia, Omar Rosario Cayetano, Juan Carlos Hernández-Gómez
Jazyk:	angličtina
Rok vydání:	2020
Předmět:	automorphism Physics and Astronomy (miscellaneous) General Mathematics Existential quantification MathematicsofComputing_GENERAL 0102 computer and information sciences 02 engineering and technology 01 natural sciences Combinatorics Computer Science::Logic in Computer Science 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) Data_FILES transitivity Mathematics domination Transitive relation Automorphism group lcsh:Mathematics 020206 networking & telecommunications Automorphism lcsh:QA1-939 Graph TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES 010201 computation theory & mathematics Chemistry (miscellaneous) Computer Science::Programming Languages γ-set Software_PROGRAMMINGLANGUAGES
Zdroj:	Symmetry Volume 12 Issue 12 Symmetry, Vol 12, Iss 2053, p 2053 (2020)
ISSN:	2073-8994
DOI:	10.3390/sym12122053
Popis:	Transitivity on graphs is a concept widely investigated. This suggest to analyze the action of automorphisms on other sets. In this paper, we study the action on the family of &gamma sets (minimum dominating sets), the graph is called &gamma transitive if given two &gamma sets there exists an automorphism which maps one onto the other. We deal with two families: paths Pn and cycles Cn. Their &gamma sets are fully characterized and the action of the automorphism group on the family of &gamma sets is fully analyzed.
Databáze:	OpenAIRE
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