On the Inclusion Ideal Graph of Semigroups  

作　　者：Barkha Baloda Jitender Kumar 

机构地区：[1]Department of Mathematics,Birla Institute of Technology and Science Pilani,Pilani,India

出　　处：《Algebra Colloquium》2023年第3期411-428,共18页代数集刊（英文版）

摘　　要：The inclusion ideal graph In(S)of a semigroup S is an undirected simple graph whose vertices are all the nontrivial left ideals of S and two distinct left ideals I,J are adjacent if and only if either I⊂J or J⊂I.The purpose of this paper is to study algebraic properties of the semigroup S as well as graph theoretic properties of In(S).We investigate the connectedness of In(S)and show that the diameter of In(S)is at most 3 if it is connected.We also obtain a necessary and sufficient condition of S such that the clique number of In(S)is the number of minimal left ideals of S.Further,various graph invariants of In(S),viz.perfectness,planarity,girth,etc.,are discussed.For a completely simple semigroup S,we investigate properties of In(S)including its independence number and matching number.Finally,we obtain the automorphism group of In(S).

关 键 词：SEMIGROUP IDEAL completely simple semigroup graph automorphism 

分 类 号：O15[理学—数学]