Groupe d’études et de recherche en analyse des décisions

# Variable Neighborhood Search for Extremal Graphs. 12. A Note on the Variance of Bounded Degrees in Graphs

## Pierre Hansen, Hadrien Mélot et Ivan Gutman

An upper bound is given on the variance of degrees of graphs with n vertices, m edges and maximum degree Δ. Particular cases of chemical interest, i.e., graphs with Δ = 3 or 4 and at most 2 cycles are examined, and conditions for the bound to be sharp derived.

, 15 pages