乘积图和F-Sum图的Steiner K-距离
Steiner K-Distances in Graph Products and F-Sum Graphs
DOI: 10.12677/PM.2023.135151, PDF,    国家自然科学基金支持
作者: 胡玲莉：浙江理工大学理学院，浙江 杭州；颜 娟：丽水学院数学与计算机学院，浙江 丽水；陈娅红*：浙江理工大学理学院，浙江 杭州；丽水学院数学与计算机学院，浙江 丽水
关键词: Steiner距离；Steiner半径；Corona积；Cluster积；F-sum图；Steiner Distance； Steiner k-Radius； Corona Product； Cluster Product； F-Sum Graphs
摘要: 图的距离是图论中非常重要且基本的概念，是研究基于距离的图不变量的基础。Steiner距离是图论组合研究中的经典问题。本文运用Steiner树的定义证明了corona积的Steiner k-半径和cluster积的Steiner k-半径的上下界以及F-sum图的Steiner距离和Steiner k-直径的界。
Abstract: Graph distance is a very important and basic concept in graph theory, which is the basis of studying graph invariants based on distance. Steiner distance is a classic problem in graph theory com-binatorial research. This paper proves the upper and lower bounds of Steiner k-radius of corona product and cluster product and the bounds of Steiner distance and Steiner k-diameter of F-sum graphs by using the definition of Steiner tree.
文章引用：胡玲莉, 颜娟, 陈娅红. 乘积图和F-Sum图的Steiner K-距离[J]. 理论数学, 2023, 13(5): 1483-1491. https://doi.org/10.12677/PM.2023.135151

参考文献

[1] Chartrand, G., Oellermann, O.R., Tian, S., et al. (1989) Steiner Distance in Graphs. Časopis Pro Pěstování Matematiky, 114, 399-410. [Google Scholar] [CrossRef] 
[2] Mao, Y.P., Cheng, E. and Zhao, W. (2017) Steiner Distance in Product Networks. Discrete Mathematics & Theoretical Computer Science, 20, Article No. 8.
[3] Wang, Z., Mao, Y.P., Melekian, C., et al. (2019) Steiner Distance in Join, Corona, Cluster, and Threshold Graphs. Journal of Information Science and Engineering, 35, 721-735.
[4] Mao, Y.P. (2017) The Steiner Diameter of a Graph. Bulletin of the Iranian Mathematical Society, 43, 439-454.
[5] Mao, Y.P., Melekian, C. and Cheng, E. (2018) A Note on the Steiner (n-k)-Diameter of a Graph. International Journal of Computer Mathematics Computer Systems Theory, 3, 41-46. [Google Scholar] [CrossRef] 
[6] Wang, Z., Mao, Y.P., Li, H.Z. and Ye, C.F. (2018) On the Steiner 4-Diameter of Graphs. Journal of Interconnection Networks, 18, Article ID: 1850002. [Google Scholar] [CrossRef] 
[7] Oellermann, O.R. and Tian, S. (2010) Steiner Centers in Graphs. Journal of Graph Theory, 14, 585-597. [Google Scholar] [CrossRef] 
[8] Eliasi, M. and Taeri, B. (2009) Four New Sums of Graphs and Their Wiener Indices. Discrete Applied Mathematics, 157, 794-803. [Google Scholar] [CrossRef] 
[9] Ashrafi, A.R., Hamzeh, A. and Hossein-Zadeh, S. (2011) Com-puting Zagreb, Hyper-Wiener and Degree-Distance Indices of Four New Sums of Graphs. Carpathian Journal of Mathematics, 27, 153-164. [Google Scholar] [CrossRef] 
[10] Kuziak, D., Yero, I.G. and Rodriguez-Velazquez, J.A. (2013) On the Strong Metric Dimension of Corona Product Graphs and Join Graphs. Discrete Applied Mathematics, 161, 1022-1027. [Google Scholar] [CrossRef] 
[11] Feng, M. and Wang, K. (2014) Identifying Codes of Corona Product Graphs. Discrete Applied Mathematics, 169, 88-96. [Google Scholar] [CrossRef] 
[12] An, M., Xiong, L. and Das, K.C. (2014) Two Upper Bounds for the Degree Distances of Four Sums of Graphs. Filomat, 28, 579-590. [Google Scholar] [CrossRef] 
[13] Feng, M. and Kong, Q. (2018) On the Fractional Metric Dimension of Corona Product Graphs and Lexicographic Product Graphs. ARS Combinatoria: An Australian Canadian Journal of Combinatorics, 138, 249-260.
[14] Aruvi, M., Joseph, J.M. and Ramganesh, E. (2021) Four New Sums of Second Hyper Zagreb Index Based on Cartesian Product. Communications in Mathematics and Applications, 12, 253-262.
[15] Patil, S. and Basavanagoud, B. (2022) Generalized Four New Sums of Graphs and Their Zagreb Indices. Discrete Mathematics, Algorithms and Applications, 14, Article ID: 2150095. [Google Scholar] [CrossRef] 
[16] Agnes, V.S. (2015) Degree Distance and Gutman Index of Corona Product of Graphs. Transactions on Combinatorics, 4, 11-23.
[17] 吕怡妃, 李俊, 黄达含, 陈娅红. F-sum图的零阶Randic指数与边度指数[J]. 丽水学院学报, 2019, 41(2): 1-12.
[18] Liu, J.B., Imran, M., Baby, S., et al. (2022) Graph Indices for Cartesian Product of f-Sum of Connected Graphs. Combinatorial Chemistry & High Throughput Screening, 25, 528-535. [Google Scholar] [CrossRef] [PubMed]
[19] Mao, Y.P. and Furtula, B. (2021) Steiner Distance in Chemical Graph Theory. Match-Communications in Mathematical and in Computer Chemistry, 86, 211-287.

为你推荐