JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 155-159.doi: 10.6040/j.issn.1671-9352.0.2022.095

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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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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

CLC Number: 

  • O157.5

Table 1

Parametric solutions in Corollary 3.2"

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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