The g-good-neighbor connectivityof G is a generalization of the concept of
connectivity, which is just for, and an important parameter in measuring the fault tolerance
and reliability of interconnection network. Many well-known networks can be
constructed by the Cartesian products of some simple graphs. In this paper, we
determine the g-good-neighbor
connectivity of some Cartesian product graphs. We give the exact value of g-good-neighbor connectivity of the
Cartesian product of two complete graphsand for , meshfor , cylindrical gridand torus for .
References
[1]
Fàbrega, J. and Fiol, M.A. (1996) On the Extra Connectivity of Graphs. Discrete Mathematics, 155, 49-57. https://doi.org/10.1016/0012-365X(94)00369-T
[2]
Peng, S.-L., Lin, C.-K., Tan, J.J.M. and Hsu, L.-H. (2012) The g-Good-Neighbor Conditional Diagnosability of Hypercube under PMC Model. Applied Mathematics and Computation, 218, 10406-10412. https://doi.org/10.1016/j.amc.2012.03.092
[3]
Wang, S.Y., Wang, Z.H. and Wang, M.J.S. (2017) The 2-Good-Neighbor Connectivity and 2-Good-Neighbor Diagnosability of Bubble-Sort Star Graph Networks. Discrete Applied Mathematics, 217, 691-706. https://doi.org/10.1016/j.dam.2016.09.047
[4]
Ren, Y.X. and Wang, S.Y. (2017) The 1-Good-Neighbor Connectivity and Diagnosability of Locally Twisted Cubes. Chinese Quarterly Journal of Mathematics, 32, 371-381.
[5]
Ren, Y.X. and Wang, S.Y. (2017) The g-Good-Neighbor Diagnosability of Locally Twisted Cubes. Theoretical Computer Science, 697, 91-97. https://doi.org/10.1016/j.tcs.2017.07.030
[6]
Wei, Y.L. and Xu, M. (2018) The 1,2-Good-Neighbor Conditional Diagnosabilities of Regular Graphs. Applied Mathematics and Computation, 334, 295-310. https://doi.org/10.1016/j.amc.2018.04.014
[7]
Wang, S.Y. and Wang, M.J.S. (2019) The g-Good-Neighbor and g-Extra Diagnosability of Networks. Theoretical Computer Science, 773, 107-114. https://doi.org/10.1016/j.tcs.2018.09.002
[8]
El-Mesady, A. and Bazighifan, O. (2022) Construction of Mutually Orthogonal Graph Squares Using Novel Product Techniques. Journal of Mathematics, 2022, Article ID: 9722983. https://doi.org/10.1155/2022/9722983
[9]
El-Mesady, A. and Shaaban, S.M. (2021) Generalization of MacNeish’s Kronecker Product Theorem of Mutually Orthogonal Latin Squares. AKCE International Journal of Graphs and Combinatorics, 18, 117-122. https://doi.org/10.1080/09728600.2021.1966349
[10]
El-Mesady, A., Bazighifan, O. and Al-Mdallal, Q. (2022) On Infinite Circulant-Balanced Complete Multipartite Graphs Decompositions Based on Generalized Algorithmic Approaches. Alexandria Engineering Journal, 61, 11267-11275. https://doi.org/10.1016/j.aej.2022.04.022
[11]
El-Shanawany, R., Higazy, M. and El-Mesady, A. (2013) On Cartesian Products of Orthogonal Double Covers. International Journal of Mathematics and Mathematical Sciences, 2013, Article ID: 265136. https://doi.org/10.1155/2013/265136
[12]
El-Mesady, A., Farahat, T. and El-Shanawany, R. (2021) Construction of the Enormous Complete Bipartite Graphs and Orthogonal Double Covers Based on the Cartesian Product. 2021 International Conference on Electronic Engineering (ICEEM), Menouf, 3-4 July 2021, 1-4. https://doi.org/10.1109/ICEEM52022.2021.9480620
[13]
El-Shanawany, R.A., Higazy, M. and Shabana, H. (2015) Cartesian Product of Two Symmetric Starter Vectors of Orthogonal Double Covers. AKCE International Journal of Graphs and Combinatorics, 12, 59-63. https://doi.org/10.1016/j.akcej.2015.06.009
[14]
Wang, Z., Mao, Y.P., Hsieh, S.-Y. and Wu, J.C. (2019) On the g-Good-Neighbor Connectivity of Graphs. Theoretical Computer Science, 804, 139-148. https://doi.org/10.1016/j.tcs.2019.11.021
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, and an important parameter in measuring the fault tolerance
and reliability of interconnection network. Many well-known networks can be
constructed by the Cartesian products of some simple graphs. In this paper, we
determine the g-good-neighbor
connectivity of some Cartesian product graphs. We give the exact value of g-good-neighbor connectivity of the
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