Item: Corona Product in Signed Graph Theory: Modelling, Structural Balance, and Control
No Thumbnail Available
Date
2025-05-03
Researcher
Singh, Amrik
Supervisor
Yadav, Sandeep Kumar
Journal Title
Journal ISSN
Volume Title
Publisher
Indian Institute of Technology, Jodhpur
Abstract
Signed networks help in studying complex relationships and interactions in various domains, offering insights into the dynamics of positive and negative influences within interconnected systems. I extend the concept of the corona product of two graphs to signed graphs, building on the marked graph framework introduced by Beineke and Harary in 1978. This approach provides a visual method for understanding the process of network generation, aiding in the analytical determination of the resulting signed graph properties. I explore both the structural and spectral properties of the corona product of signed graphs. Additionally, I introduce the concept of signed corona graphs, which are formed by iteratively applying the corona product to a fixed small signed graph, known as the seed graph. These signed corona graphs serve as a model for generating large, evolving signed networks. This study includes an examination of the structural properties of corona graphs, such as the statistics of signed edges, various types of signed triangles, and degree distribution. I also investigate the algebraic conflict within signed corona graphs produced by specially structured seed graphs. By carefully selecting a seed graph, it is possible to generate corona graphs that mirror the properties of real-world signed networks. I have expanded the corona product of signed graphs into a generalized corona product of signed graphs motivated by the generalized corona product of unsigned graphs. I study the structural balance and spectral properties of these graphs. By utilizing the notion of coronal of a graph, I determine the formulas of characteristic, Laplacian, and signless Laplacian polynomials of eneralized corona product of signed graphs. I have also identified sufficient conditions for the generalized corona product of some special collections of signed graphs to be co-spectral. Following this, I analyze the controllability of the corona product of signed graphs and derive sufficient conditions based on the spectra of corona product of signed graphs.
Description
Keywords
Citation
Singh, Amrik (2014).Corona Product in Signed Graph Theory: Modelling, Structural Balance, and Control (Doctor's thesis). Indian Institute of Technology Jodhpur