Abstract
Using coalescence and cones, this study defines three types of graphs formed by amalgamating vertices of disjoint unions of complete graphs. The three types include the cone over a disjoint union of two complete graphs (C1), the cone over a disjoint union of k complete graphs (C2), and the l cone over a disjoint union of two complete graphs (C3). Coalescence of complete graphs (C1, C3) and the l
cone (C3) are determined by their Laplacian spectra, a novel finding. Their Laplacian spectra reveal the size of the vertex cutset. Applications include the analysis of corporate networks, where individuals form coalescence of complete graphs through joint membership of two or more company boards.
cone (C3) are determined by their Laplacian spectra, a novel finding. Their Laplacian spectra reveal the size of the vertex cutset. Applications include the analysis of corporate networks, where individuals form coalescence of complete graphs through joint membership of two or more company boards.
| Original language | English |
|---|---|
| Pages (from-to) | 25-39 |
| Number of pages | 15 |
| Journal | Open Journal of Discrete Applied Mathematics |
| Volume | 6 |
| Issue number | 1 |
| Early online date | 30 Apr 2023 |
| DOIs | |
| Publication status | Published - 30 Apr 2023 |
Bibliographical note
Acknowledgments: I would like to thank Nicole Snashall for her encouragement, comments and support. I also would like to thank Jozef Siran for his comments on amalgamations, which led to more thinking about defining my graphs. Thisproject started with an application to social networks; however, it developed into a much more general study. I would like to dedicate this paper to the memory of Alto Zeitler (1945-2022), my mathematics teacher.
Keywords
- Coalescence
- Laplacian spectrum
- Block graphs