线形图的Kronecker积的代数连通性

IF 0.6 Q4 MATHEMATICS, APPLIED

Discrete Mathematics Algorithms and Applications Pub Date : 2023-08-11 DOI:10.1142/s1793830923500751

Shivani Chauhan, A. Satyanarayana Reddy

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引用次数: 0

摘要

设$X$是一棵有$n$顶点的树，$L(X)$是它的线形图。在这项工作中，我们完全刻画了L(X)\乘以K_m$的代数连通性等于$m-1$的树，其中$\乘以$表示Kronecker积。给出了L(X) * K_m为拉普拉斯积分的几个充要条件。讨论了L(X)\乘以K_m$的代数连通性，其中$X$是直径$4$的树和$k$-book图。

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Algebraic connectivity of Kronecker products of line graphs

Let $X$ be a tree with $n$ vertices and $L(X)$ be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of $L(X)\times K_m$ is equal to $m-1$, where $\times$ denotes the Kronecker product. We provide a few necessary and sufficient conditions for $L(X)\times K_m$ to be Laplacian integral. The algebraic connectivity of $L(X)\times K_m$, where $X$ is a tree of diameter $4$ and $k$-book graph is discussed.

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来源期刊

Discrete Mathematics Algorithms and Applications MATHEMATICS, APPLIED-

CiteScore

1.50

自引率

41.70%

发文量

129