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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (11): 155-159.doi: 10.6040/j.issn.1671-9352.0.2022.095

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基于完全图构造的两类整图

王力工1(),郁志明1,*(),周枫2,陶丽杰1,邢露淇3   

  1. 1. 西北工业大学数学与统计学院, 陕西 西安 710129
    2. 西北工业大学教育实验学院, 陕西 西安 710129
    3. 西北工业大学管理学院, 陕西 西安 710129
  • 收稿日期:2022-02-07 出版日期:2023-11-20 发布日期:2023-11-07
  • 通讯作者: 郁志明 E-mail:lgwang@nwpu.edu.cn;yzm2020303246@mail.nwpu.edu.cn
  • 作者简介:王力工(1968—)，男，教授，研究方向为图论及其应用. E-mail：lgwang@nwpu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11871398);陕西省大学生创新创业训练计划资助项目(S202110699704)

Two kinds of integral graphs based on complete graphs

Ligong WANG1(),Zhiming YU1,*(),Feng ZHOU2,Lijie TAO1,Luqi XING3   

  1. 1. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710129, Shaanxi, China
    2. Honors College, Northwestern Polytechnical University, Xi'an 710129, Shaanxi, China
    3. School of Management, Northwestern Polytechnical University, Xi'an 710129, Shaanxi, China
  • Received:2022-02-07 Online:2023-11-20 Published:2023-11-07
  • Contact: Zhiming YU E-mail:lgwang@nwpu.edu.cn;yzm2020303246@mail.nwpu.edu.cn

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摘要：

定义了两类新图q * Kn与K1, m ·(q * Kn)。利用粘接图的特征多项式性质得到了这两类图的特征多项式，并刻画了这两类图为整图的含参数充要条件，进而也给出了它们为整图的一些充分条件。

关键词: 整图, 邻接矩阵, 特征多项式, 完全图

Abstract:

Two kinds of new graphs q * Kn and K1, m·(q * Kn) are defined. We obtain their characteristic polynomials by using the properties of characteristic polynomials of coalescence of graphs. We also characterize sufficient and necessary conditions with parameters for these graphs to be integral. Furthermore, some sufficient conditions for these graphs to be integral are presented.

Key words: integral graph, adjacency matrix, characteristic polynomial, complete graph

中图分类号: 

  • O157.5

表1

推论3.2中的参数解"

m n q a b c m n q a b c
5 5 2 5 1 -3 10 10 2 10 2 -4
10 4 3 5 1 -4 28 7 6 10 2 -7
28 4 9 8 1 -7 60 5 7 10 2 -9
21 5 10 9 1 -7 54 6 3 9 3 -8
33 5 16 11 1 -9 33 9 4 11 3 -7
55 4 18 11 1 -10 44 8 5 11 3 -8
20 5 2 6 2 -5 88 7 3 11 4 -10
28 5 3 7 2 -6 45 9 1 9 5 -7
16 7 3 8 2 -5 60 8 1 9 5 -8
24 6 4 8 2 -6 55 10 2 11 5 -8
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