LINE GRAPHS OF COMPLEX UNIT GAIN GRAPHS WITH LEAST EIGENVALUE-2

被引：0
|
作者：
Belardo, Francesco [1 ]
Brunetti, Maurizio [1 ]
机构：
[1] Univ Naples Federico II, Dept Math & Applicat, Naples, Italy
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2021年 / 37卷
关键词：
Complex unit gain graph; Line graph; Subdivision graph; Oriented gain graph; Voltage graph; Star complement technique;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let T be the multiplicative group of complex units, and let L(Phi) denote a line graph of a T-gain graph Phi. Similarly to what happens in the context of signed graphs, the real number min Spec(A(L(Phi)), that is, the smallest eigenvalue of the adjacency matrix of L(Phi)), is not less than -2. The structural conditions on Phi ensuring that min Spec(A(L(Phi)) = -2 are identified. When such conditions are fulfilled, bases of the -2-eigenspace are constructed with the aid of the star complement technique.
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页码：14 / 30
页数：17
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