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首页> 外文期刊>Bulletin of the Chemical Society of Japan >Eigenspectral analysis of pendant vertex- and pendant edge-weighted graphs of linear chains, cycles, and stars
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Eigenspectral analysis of pendant vertex- and pendant edge-weighted graphs of linear chains, cycles, and stars

机译：线性链，周期和恒星的垂线顶点和垂线边缘加权图的本征谱分析

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摘要

Three classes of pendent vertex- and pendant edge-weighted graphs of linear chains (class I), stars (class II), and cycles (class III) have been presented. These graphs (particularly class I and III) represent heteroconjugated pi-systems. Sometimes such graphs appear as factored subgraphs of some complicated graphs. The eigenspectra of these graphs have been found out in analytical forms. These eigenspectra have been utilized i) to calculate the band (i.e., HOMO-LUMO) gaps of such graphs, ii) to find out three classes of inversely proportional graphs (with inversely proportional pairs of eigenvalues), and iii) to express eigenspectra of some complicated graphs in analytical forms along with some subspectral relationships. In the limit of n (number of vertices) to infinity, the band gap of the graph of class I has been shown to be the same with that calculated by considering its hypothetical "cyclic dimer." Reciprocal graphs have also been considered in this context. These graphs are not all hypothetical. A few of them have also been synthesized.
机译：提出了线性链（I类），星形（II类）和周期（III类）的三类悬垂顶点和垂线边缘加权图。这些图（特别是I和III类）表示异共轭pi系统。有时，这些图会显示为某些复杂图的分解子图。这些图的本征谱已经以分析形式找到。这些特征谱已被用于：i）计算此类图的带隙（即HOMO-LUMO），ii）找出三类反比例图（具有特征值的反比例对），和iii）表示图谱的本征谱分析形式的一些复杂图形以及一些次光谱关系。在n（顶点数）到无穷大的限制内，I类图的带隙与考虑其假设的“循环二聚体”所计算的带隙相同。在这种情况下，也考虑了倒数图。这些图并非都是假设的。其中一些也已合成。

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