More results on degree deviation and degree variance

‎This paper investigates degree deviation and variance in graph theory‎, ‎with a specific focus on k-regular graphs and subdivision of graphs‎. ‎These metrics are fundamental for characterizing graph irregularity and have significant applications in network analysis and the social sciences‎.‎Furthermore‎, ‎we introduce novel geometric measures of irregularity‎, ‎geometric degree deviation and geometric degree variance derived from the geometric mean of vertex degrees‎.‎By means of rigorous theorems and illustrative examples‎, ‎we explore the relationships between graph structures and their degree properties‎. ‎Our findings seek to advance the current understanding of graph irregularity and provide a solid foundation for future research in this area‎.

کلیدواژه ها:

Irregularity‎ ، ‎Degree deviation ، ‎Degree variance