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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (6): 655-671.doi: 10.3969/j.issn.1005-3085.2017.06.009

• • 上一篇    下一篇

一些路的计数技巧与图的广义谱（英）

刘奋进1,2,   王   卫2   

  1. 1- 长安大学理学院，西安  710064
    2- 西安交通大学数学与统计学院，西安  710049
  • 收稿日期:2015-10-26 接受日期:2017-02-27 出版日期:2017-12-15 发布日期:2018-02-15
  • 基金资助:
    国家自然科学基金(11401044;11471005;11501050)；国家博士后科学基金(2014M560754)；陕西省博士后科学基金和中央高校基础研究基金(310812161006).

Enumeration Technique for Some Paths and Generalized Spectrum of a Graph

LIU Fen-jin1,2,   WANG Wei2   

  1. 1- School of Science, Chang'an University, Xi'an 710064
    2- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2015-10-26 Accepted:2017-02-27 Online:2017-12-15 Published:2018-02-15
  • Supported by:
    The National Natural Science Foundation of China (11401044; 11471005; 11501050); the Postdoctoral Science Foundation of China (2014M560754); the Postdoctoral Science Foundation of Shaanxi and the Fundamental Research Funds for the Central Universities (310812161006).

PDF (PC)

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摘要： 一个图$X$称为是由它的广义谱确定的，如果对任意图$H$，$H$与$X$同谱且补图同谱蕴含$H$与$X$同构．本文给出了任意图中长度不超过5的路的计数公式，并且证明了当$k\not\equiv2$ (mod 3)时，格子图$P_k\square P_2$是由它的广义谱确定的．

关键词: 广义谱, 广义同谱, 广义谱确定, 格子图

Abstract: A graph $X$ is said to be determined by its generalized spectrum if for any graph $H$, $H$ and $X$ being cospectral with cospectral complements implies that $H$ is isomorphic to $X$. This paper determines formulas for enumerating the number of paths with length no more than $5$ in any graph and proves that if $k\not\equiv2$ (mod 3), then the grid graph $P_k\square P_2$ is determined by its generalized spectrum.

Key words: generalized spectrum, generalized cospectral, determined by generalized spectrum, grid graph

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