JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (6): 40-45, 76.doi: 10.6040/j.issn.1671-9352.0.2021.454

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Graph N[S]-T reconstruction based on neighbor connectivity optimization

Le CHANG(),Zongtian WEI   

  1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, Shaanxi, China
  • Received:2021-06-28 Online:2023-06-20 Published:2023-05-23

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Abstract:

Considering the neighbor invulnerability recovery of a damaged network based on the optimization idea, the neighbor subversion strategy and the concept of reconstruction are proposed. The problem of graph reconstruction based on neighbor connectivity optimization is studied. An optimal reconstruction method and an algorithm of Cartesian product graph of two complete graphs under the optimal neighbor subversion strategy are presented.

Key words: neighbor subversion strategy, reconstruction, optimal reconstruction, complete graph, cartesian product graph

CLC Number: 

  • O157.5

Fig.1

(a) Cycle C9, (b) after subversion, (c) the optimal reconstruction of C9"

Fig.2

(a) Tree G, (b) after subversion, (c) an optimal reconstruction of G"

Fig.3

(a) Path P8, (b) after subversion, (c) and (d) two different optimal reconstructions of P8"

Fig.4

Optimal reconstruction of K9×K3"

Fig.5

Optimal reconstruction of K9×K6"

1 COZZENS M B , WU S . Extreme values of the edge-neighbor-connectivity[J]. ARS Combinatoria-Waterloo then Winnipeg-, 1995, 39 (1): 199- 210.
2 GUNTHER G , HATNELL B L . On m-connected and k-neighbor-connected graphs[J]. Graph Theory, Combinatorics and Applications, 1991, 2, 585- 596.
3 TUTTE W T . The reconstruction problem in graph theory[J]. British Polymer Journal, 1977, 9 (3): 180- 183.
doi: 10.1002/pi.4980090302
4 ABDALLAH M , HUNG C N . Neighbor connectivity of the alternating group graph[J]. Journal of Interconnection Networks, 2021, 2150014.
5 SHANG Y J , HAO R X , GU M M . Neighbor connectivity of two kinds of cayley graphs[J]. Acta Mathematicae Applicatae Sinica, English Series, 2018, 34 (2): 386- 397.
doi: 10.1007/s10255-018-0739-9
6 WANG M , LIN Y , WANG S . The 1-good-neighbor connectivity and diagnosability of Cayley graphs generated by complete graphs[J]. Discrete Applied Mathematics, 2017, 246 (9): 108- 118.
7 GUNTHER G . Neighbour-connectivity in regular graphs[J]. Discrete Applied Mathematics, 1985, 11 (3): 233- 243.
8 BONDY J A , MURTY U S R . Graph theory with applications[M]. London: Springer, 2008.
9 魏宗田, 刘勇. 网络抗毁性[M]. 西安: 西安交通大学出版社, 2015.
WEI Zongtian , LIU Yong . Network invulnerability[M]. Xi'an: Xi'an Jiaotong University Press, 2015.
10 WEI Zongtian , MAI Anchan , ZHAI Meijuan . Vertex-neighbor-scattering number of graphs[J]. ARS Combinatoria: An Australian-Canadian Journal of Combinatorics, 2011, 102, 417- 426.
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