arXiv subjects

Aysun Aytac

Publications and source records attributed to Aysun Aytac.

3 recordsLinked to original sources

arXiv2026

Paired Disjunctive Domination Number of Middle Graphs

The concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a transformation that captures both adjacency and incidence relations of the original graph. We begin by investigating this parameter for middle graphs of several special graph classes, including path graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs, star graphs, friendship graphs, and double star graphs. We then present general results by establishing lower and upper bounds for the paired disjunctive domination number in middle graphs of arbitrary graphs, with particular emphasis on trees. Additionally, we determine the exact value of the parameter for middle graphs obtained through the join operation. These findings contribute to the broader understanding of domination-type parameters in transformed graph structures and offer new insights into their combinatorial behavior.

cs.DM↗

arXiv2026

Analyzing Network Robustness via Residual Closeness

Networks are inherently vulnerable to vertex failures, making the analysis of their structural robustness a fundamental problem in graph theory. In this study, we investigate the closeness and vertex residual closeness of graphs, with a particular focus on the middle graph representations of certain special graph classes, which provide a richer structural framework for analysis. We derive exact expressions for the closeness values of these middle graphs and determine their residual closeness under vertex failures. By utilizing results obtained from specific graph families, we establish several general bounds for broader graph classes. Furthermore, by exploiting the relationship between the closeness of a graph, its line graphs, and middle graphs, we obtain new results that relate these three structures. In addition, we propose an algorithm for computing closeness in middle graphs and provide a detailed analysis of its performance.

cs.DM↗

arXiv2024

Closeness and Residual Closeness of Harary Graphs

Analysis of a network in terms of vulnerability is one of the most significant problems. Graph theory serves as a valuable tool for solving complex network problems, and there exist numerous graph-theoretic parameters to analyze the system's stability. Among these parameters, the closeness parameter stands out as one of the most commonly used vulnerability metrics. Its definition has evolved to enhance the ease of formulation and applicability to disconnected structures. Furthermore, based on the closeness parameter, vertex residual closeness, which is a newer and more sensitive parameter compared to other existing parameters, has been introduced as a new graph vulnerability index by Dangalchev. In this study, the outcomes of the closeness and vertex residual closeness parameters in Harary Graphs have been examined. Harary Graphs are well-known constructs that are distinguished by having $n$ vertices that are $k$-connected with the least possible number of edges.

cs.DM↗