Closeness of some tree structures

Tunçel Gölpek H.

SOFT COMPUTING, vol.1, no.1, pp.1-13, 2023 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 1 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s00500-023-09395-z
  • Journal Name: SOFT COMPUTING
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, zbMATH
  • Page Numbers: pp.1-13
  • Dokuz Eylül University Affiliated: Yes

Abstract

The vulnerability analysis of networks is a central goal within the concept of graph-theoretic problems. Therefore, graph theory serves as an essential scientific tool for studying the reliability and robustness of networks. Vertex centrality has great importance in the context of network analysis. One of the metrics used in network analysis is closeness centrality, which is a structural measure that evaluates the importance of a node in a network. This measure is based on the sum of the distances between the node and all other nodes in the network. This paper analyzes the closeness of different tree structures. In addition, formulas for the closeness of k-ary trees, binomial trees, comet graphs, double comet graphs, double star graphs, and Et p graphs are established. Upper and lower bounds are studied for k-ary and binary trees. Upper bounds arise from the perfect form of the tree for the k-ary tree and its special structure of the binary tree. Moreover, some numerical experiments are conducted on the considered graph structures. The results are supported the robustness of the double star graph structure in terms of closeness centrality. Furthermore, we present a relevant application problem within the context of this study.