2016•Discrete Mathematics Algorithms and ApplicationsRequires access

Domination in total graphs of small rings

Alpesh M. Dhorajia, Jimmy M. Morzaria

Abstract

Let [Formula: see text] be a commutative ring and [Formula: see text] be its set of zero divisors. The total graph of [Formula: see text] (introduced by Anderson and Badawi) denoted by [Formula: see text]. For any positive integers [Formula: see text] and [Formula: see text] we obtain the domination number of the total graph of [Formula: see text]. We also obtain various domination parameters including [Formula: see text] and [Formula: see text]. Finally we explore domination parameters in the complement of the total graph [Formula: see text].

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Key concepts: Mathematics, Combinatorics, Graph, Complement (music), Domination analysis, Zero divisor, Commutative ring, Discrete mathematics