论文标题
在布兰特半群的通勤图上
On the commuting graphs of Brandt semigroups
论文作者
论文摘要
由δ表示有限的非共同半群的通勤图是一个简单的图形，其顶点是s的非中央元素和两个不同的顶点x。如果xy = yx，则y相邻。在本文中，我们研究了Brandt Semigroup b_n的通勤图δ（B_N）的各种图理论特性，包括其直径，集团数，色数，独立数，独立性，强度度度和优势数量。此外，我们获得了δ（bn）的自动形态组AUT（δ（bn））和内态单态端（δ（bn））。我们表明aut（δ（bn））= s_n \ times z_2，其中s_n是n和z_2的对称组，是整数模拟2的添加剂组。此外，对于n \ geq 4，我们证明了端（δ（Δ（bn））= aut（δ（bn））。为了对[2]中提出的问题提供答案，我们确定了一类逆半群，其通勤图为哈密顿量。
The commuting graph of a finite non-commutative semigroup S, denoted by Δ(S), is the simple graph whose vertices are the non-central elements of S and two distinct vertices x; y are adjacent if xy = yx. In the present paper, we study various graph-theoretic properties of the commuting graph Δ(B_n) of Brandt semigroup B_n including its diameter, clique number, chromatic number, independence number, strong metric dimension and dominance number. Moreover, we obtain the automorphism group Aut(Δ(Bn)) and the endomorphism monoid End(Δ(Bn)) of Δ(Bn). We show that Aut(Δ(Bn)) = S_n \times Z_2, where S_n is the symmetric group of degree n and Z_2 is the additive group of integers modulo 2. Further, for n \geq 4, we prove that End(Δ(Bn)) =Aut(Δ(Bn)). In order to provide an answer to the question posed in [2], we ascertained a class of inverse semigroups whose commuting graph is Hamiltonian.
