Open AccessArc and twin arc domination in Cayley digraphs
Author(s) -
R. Rajeswari,
R. Anbunathan
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1770/1/012076
Subject(s) - arc (geometry) , digraph , combinatorics , mathematics , cardinality (data modeling) , domination analysis , path (computing) , dominating set , cayley graph , enhanced data rates for gsm evolution , generating set of a group , discrete mathematics , graph , geometry , computer science , vertex (graph theory) , telecommunications , data mining , programming language
Let G be a finite group and let S be a generating subset of G. The Cayley digraph Cay (G, S) is the digraph with node set as the elements of G and there is an arc from u to us whenever u ϵ G and s ϵ S. An arc e1 in a digraph D out arc dominates itself as well as all arcs ei. Such that {e 1 , e i } is a directed path of length 2 in D. While e1 in arc dominates both itself and all arcs ej such that {e i , e 1 } is a directed path of length 2 in D. The arc domination number is the minimum cardinality of an out arc dominating set of D denoted by γ′ ( D ). A set of edges of D is twin arc dominating set if every edge of D is out arc dominated by some edge of S and in arc dominated by some edge of S. The minimum Cardinality of a twin arc dominating set is the twin arc domination number denoted by γ * ( D ) of D. This paper discusses the arc domination and twin arc domination of Cayley digraphs and attempts to find bounds for the arc domination number of the same class of graphs.