

on the small intersection graph of submodules of a module





نویسنده

talebi yahya ,mahdavi lotf ali

منبع

journal of algebraic structures and their applications  2021  دوره : 8  شماره : 1  صفحه:117 130

چکیده

Let m be a unitary left rmodule, where r is a (not necessarily commutative) ring with identity. the small intersection graph of nontrivial submodules of m, denoted by γ(m), is an undirected simple graph whose vertices are in onetoone 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.

کلیدواژه

complemented graph ,domination number ,orthogonal vertex ,planar ,small intersection graph

آدرس

university of mazandaran, faculty of mathematical sciences, department of mathematics, iran, university of mazandaran, faculty of mathematical sciences, department of mathematics, iran

پست الکترونیکی

l.a.mahdavi154@gmail.com












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