2023/07/19 by Kavya R. Nair, Nair, Kavya. R., M. S. Sunitha +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2307.10407
openalex publication_date 2023/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concepts of domination and topological index hold great significance within the realm of graph theory. Therefore, it is pertinent to merge these concepts to derive the domination index of a graph. A novel concept of the domination index is introduced, which utilizes the domination degree of a vertex. The domination degree of a vertex a is defined as the minimum cardinality of a minimal dominating set that includes a. The idea of domination degree and domination index is conducted of graphs like complete graphs, complete bipartite, r partite graphs, cycles, wheels, paths, book graphs, windmill graphs, Kragujevac trees. The study is extended to operation in graphs. Inequalities involving domination degree and already established graph parameters are discussed. An application of domination degree is discussed in facility allocation in a city. Algorithm to find a MDS containing a particular vertex is also discussed in the study.