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关于自环图能量的新下界
New Lower Bounds on the Energy of Graphs with Self-Loops

DOI: 10.12677/pm.2025.151012, PP. 97-102

Keywords: 自环图,图能量,特征值
Graphs with Self-Loops
, Graph Energy, Eigenvalues

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Abstract:

G S n 个顶点的自环图,其通过在简单图 G 上向点集 SV( G ) 中的点添加自环得到。自环图 G S 的能量由Gutman等学者定义为 E( G S )= i=1 n | λ i σ n | ,其中 λ 1 ,, λ n G S 的邻接特征值, σ G S 中自环的个数。本文利用矩阵理论给出了一个自环图最大特征值上界的充要条件,并利用这个上界和Ozeki不等式分别给出了自环图能量 E( G S ) 的新下界。
Let G S be a self-loop graph with n vertices obtained from a simple graph G by attaching one self-loop at each vertex in

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