ON THE SMALL INTERSECTION GRAPH OF SUBMODULES OF A MODULE

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Mahdavi Lotf Ali; TALEBI YAHYA

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Journal Paper

Paper Information

Journal: Algebraic structures and their applications Year:2021 | Volume:8 | Issue:1 Page(s): 117-130

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Title

ON THE SMALL INTERSECTION GRAPH OF SUBMODULES OF A MODULE

Author(s)

Mahdavi Lotf Ali | TALEBI YAHYA | Issue Writer Certificate

Keywords

small intersection graph

planar

complemented graph

orthogonal vertex

domination number

Abstract

Let M be a unitary left R-module, where R is a (not necessarily commutative) ring with identity. The small intersection graph of nontrivial submodules of M, denoted by 􀀀, (M), is an undirected simple graph whose vertices are in one-to-one correspondence with all nontrivial submodules ofM and two distinct vertices are adjacent if and only if the intersection of corresponding submodules is a small submodule of M. In this paper, we investigate the fundamental properties of these graphs to relate the combinatorial properties of ℾ, (M) to the algebraic properties of the module M. We determine the diameter and the girth of ℾ, (M). We obtain some results for connectivity and planarity of these graphs. Moreover, we study orthogonal vertex, domination number and the conditions under which the graph ℾ, (M) is complemented.

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APA: Copy

Mahdavi, Lotf Ali, & TALEBI, YAHYA. (2021). ON THE SMALL INTERSECTION GRAPH OF SUBMODULES OF A MODULE. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, 8(1), 117-130. SID. https://sid.ir/paper/1059299/en

Vancouver: Copy

Mahdavi Lotf Ali, TALEBI YAHYA. ON THE SMALL INTERSECTION GRAPH OF SUBMODULES OF A MODULE. ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS[Internet]. 2021;8(1):117-130. Available from: https://sid.ir/paper/1059299/en

IEEE: Copy

Lotf Ali Mahdavi, and YAHYA TALEBI, “ON THE SMALL INTERSECTION GRAPH OF SUBMODULES OF A MODULE,” ALGEBRAIC STRUCTURES AND THEIR APPLICATIONS, vol. 8, no. 1, pp. 117–130, 2021, [Online]. Available: https://sid.ir/paper/1059299/en

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