链图的距离特征值

doi:10.15960/j.cnki.issn.1007-6093.2024.01.009

Abstract

Abstract:

A graph is called a chain graph if it does not contain induced $2K_2$, $C_3$ or $C_5$. In spectral graph theory, chain graphs feature as graphs whose largest eigenvalue within the connected bipartite graphs of fixed order and size is maximal. In this paper, we consider the distance eigenvalues of a connected chain graph $G$. We present that $-2$ is an eigenvalue of $G=G(t_1,\cdots,t_h; s_1,\cdots,s_h)$, with multiplicity $n-2h$. And further more, there are exactly $h-1$ eigenvalues less than -2 and exactly $h+1$ eigenvalues greater than -2.

Key words: chain graphs, distance spectrum, equitable partition

CLC Number:

O221.2

Xuezheng LYU, Mengyu MA. The distance spectra of chain graphs[J]. Operations Research Transactions, 2024, 28(1): 112-120.

Figures/Tables 2

References 16

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阶数	$ \left(t_1, \cdots, t_h; s_1, \cdots, s_h\right) $	距离谱
5	$ \left(1;4\right) $	{6.61, $ - $0.61, $ (-2)^3 $}
5	$ \left(1, 2;1, 1\right) $	{7.46, $ - $0.51, $ - $1.08, $ - $2, $ - $3.86}
5	$ \left(2, 1;1, 1\right) $	{6.54, 0, $ - $1.05, $ - $2, $ - $3.48}
6	$ \left(1, 1, 1;1, 1, 1\right) $	{9.26, 0, $ - $1, $ - $1.09, $ - $3.17, $ - $4}
6	$ \left(2, 1;1, 2\right) $	{8.57, 0.36, $ - $1, $ (-2)^2 $, $ - $3.93}
6	$ \left(2, 2;1, 1\right) $	{8.90, 0, $ - $0.9, $ (-2)^2 $, $ - $4}
6	$ \left(3;3\right) $	{7, 1, $ (-2)^4 $}
7	$ \left(1, 1, 1;1, 1, 2\right) $	{11.77, 0, $ - $0.85, $ - $1.07, $ - $2, $ - $3.26, $ - $4.59}
7	$ \left(2, 1, 1;1, 1, 1\right) $	{10.53, 0.58, $ - $0.77, $ - $1.03, $ - $2, $ - $3.19, $ - $4.12}
7	$ \left(2, 2;1, 2\right) $	{11.19, 0.36, $ - $0.85, $ (-2)^3 $, $ - $4.69}
7	$ \left(4;3\right) $	{8.61, 1.39, $ (-2)^5 $}
8	$ \left(4;4\right) $	{10, 2, $ (-2)^6 $}
8	$ \left(2, 2;2, 2\right) $	{12.32, 0.83, $ - $0.32, $ (-2)^4 $, $ - $4.83}

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The distance spectra of chain graphs

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