关于自环图的能量的下界
The Lower Bound on the Energy of the Self-Loops Graph
DOI: 10.12677/PM.2023.1310302, PDF,    国家自然科学基金支持
作者: 邹林芳：福建师范大学数学与统计学院，福建 福州
关键词: 特征值；自环图；能量；Eigenvalues； Self-Loops Graph； Energy
摘要: 设图G=(V(G),E(G))是阶为n的简单图。令S⊆V(G)且|S|=σ，设图GS是对图G中属于S的每个顶点增加一个自环所得到的图。图GS的能量定义为，其中λ1(GS),…,λn(GS)是图GS的邻接矩阵的特征值。在本文中，我们利用自环图的邻接矩阵的特征值的性质构造了满足不等式条件的实数序列。运用分析不等式的技巧，我们得到了自环图GS的能量E(GS)的下界。
Abstract: Let G=(V(G),E(G)) be a simple graph of order . Let S⊆V(G) and |S|=σ, and let GS be the graphobtained from G by adding a self-loop to each vertex belonging to S in graph G. The energy of GS is defined as , where λ1(GS),…,λn(GS) are the eigenvalues of the adjacency matrix of GS. In this paper, by using the property of eigenvalues of the adjacency matrix of the self-loops graph GS, we construct the sequence of real numbers satisfying some conditions of the inequality. By means of inequality analysis technique, we get the lower bound of the energy E(GS) of the self-loops graph GS.
文章引用：邹林芳. 关于自环图的能量的下界[J]. 理论数学, 2023, 13(10): 2948-2953. https://doi.org/10.12677/PM.2023.1310302

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