<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our findings are categorized based on the underlying graph’s diameter. The formula for calculating the closeness of a Mycielski graph is derived for graphs with a diameter of less than or equal to 4. Furthermore, we establish a sharp lower bound for the closeness of a Mycielski graph when the diameter of the underlying graph is greater than 4. To achieve this, the closeness of the Mycielski transformation of a path graph plays an important role. Additionally, leveraging the obtained results, we examine the closeness of a special planar construction composed of path and cycle graphs, as well as its Mycielski transformation.</p>
</abstract>

The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between every pair of vertices. Initially, we delve into a discussion about the applicability of the closeness parameter to Mycielski graphs. Our findings are categorized based on the underlying graph’s diameter. The formula for calculating the closeness of a Mycielski graph is derived for graphs with a diameter of less than or equal to 4. Furthermore, we establish a sharp lower bound for the closeness of a Mycielski graph when the diameter of the underlying graph is greater than 4. To achieve this, the closeness of the Mycielski transformation of a path graph plays an important role. Additionally, leveraging the obtained results, we examine the closeness of a special planar construction composed of path and cycle graphs, as well as its Mycielski transformation.

Computing closeness for some graphs

Dokuz Eylul University Maritime Faculty Buca Izmir

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Computing closeness for some graphs"}

The analysis of networks involves several crucial parameters. In this paper, we consider the closeness parameter, which is based on the total distance between...

Computing closeness for some graphs

Published Online: Dec 12, 2023

Page range: 221 - 238

Received: Aug 14, 2023

DOI: https://doi.org/10.2478/ausi-2023-0015

Keywords
graph vulnerability, closeness, Mycielski graph, Tadpole graph

© 2023 Hande Tunçel Gölpek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Computing closeness for some graphs

Published Online: Dec 12, 2023

Page range: 221 - 238

Received: Aug 14, 2023

DOI: https://doi.org/10.2478/ausi-2023-0015

Keywordsgraph vulnerability, closeness, Mycielski graph, Tadpole graph

© 2023 Hande Tunçel Gölpek et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
graph vulnerability, closeness, Mycielski graph, Tadpole graph