Status Sombor Indices of Unitary Cayley Graph

Objectives: The objective of the study is to obtain the values of status Sombor indices for the unitary Cayley graph. Methods: The unitary Cayley graph 𝑋𝑛 has vertex set 𝑍𝑛 = {0, 1, 2, ...𝑛 − 1}. Vertices a, and b are adjacent, if 𝑔𝑐𝑑(𝑎 − 𝑏, 𝑛) = 1. The status 𝜎 (𝑢) of a vertex u in a graph, G is the sum of distances of all other vertices from u in 𝐺. In this paper, we obtain the values of the Status Sombor index, Modified Status Sombor index, and their corresponding exponentials and compute exact formulae for unitary Cayley graph 𝑋𝑛. Findings: Different values of status Sombor indices have been obtained for unitary Cayley graphs of various orders. Novelty: The values of status Sombor indices have been extensively studied by various researchers recently and most of the research has been done for different types of graphs in chemical graph theory. The present work reveals that the unitary Cayley graph is one of the graphs that is extensively studied in both the areas of group theory and graph theory. We derive the values of status Sombor indices that are dependent on the status and degree of the vertices of the unitary Cayley graph. Mathematics Subject Classification: 05C09, 05C25, 05C50. Keywords: Unitary Cayley graphs; Status Sombor index; Modified status Sombor index; Status Sombor exponential; Modified status Sombor exponential