Domination number in the annihilating-ideal graphs of commutative rings | Zendy

R. Nikandish | Zendy; Hamid Reza Maimani | Zendy; Sima Kiani | Zendy

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Domination number in the annihilating-ideal graphs of commutative rings

Author(s) -

R. Nikandish,

Hamid Reza Maimani,

Sima Kiani

Publication year - 2015

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim140222001n

Subject(s) - mathematics , combinatorics , commutative ring , vertex (graph theory) , domination analysis , annihilator , discrete mathematics , zero divisor , graph , ideal (ethics) , primary ideal , commutative property , principal ideal ring , pure mathematics , algebra over a field , philosophy , epistemology

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R)\{0} and two distinct vertices I and J are adjacent if and only if IJ = 0. In this paper, we study the domination number of AG(R) and some connections between the domination numbers of annihilating-ideal graphs and zero-divisor graphs are given.

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