Zero divisor graphs for S-act

Haghdadi, Toktam; Estaji, Ali Akbar

doi:10.1134/s1995080215010084

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2018

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“…Recently, inclusion graphs attached to rings, vector spaces and groups have been studied in [1,8,5]. Moreover, some works associating graphs to S-acts can be found in [6,9,13].…”

Section: Introductionmentioning

confidence: 99%

On the inclusion graphs of S-acts

Delfan¹,

Rasouli²,

Tehranian³

2018

J. Math. Computer Sci.

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In this paper, we define the inclusion graph Inc(A) of an S-act A which is a graph whose vertices are non-trivial subacts of A and two distinct vertices B 1 , B 2 are adjacent if B 1 ⊂ B 2 or B 2 ⊂ B 1 . We investigate the relationship between the algebraic properties of an S-act A and the properties of the graph Inc(A). Some properties of Inc(A) including girth, diameter and connectivity are studied. We characterize some classes of graphs which are the inclusion graphs of S-acts. Finally, some results concerning the domination number of such graphs are given.

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“…Recently, inclusion graphs attached to rings, vector spaces and groups have been studied in [1,8,5]. Moreover, some works associating graphs to S-acts can be found in [6,9,13].…”

Section: Introductionmentioning

confidence: 99%