Core Concepts
The author explores extremal chemical graphs for the arithmetic-geometric index, providing upper bounds and characterizations.
Abstract
The content delves into the arithmetic-geometric index as a degree-based graph invariant in mathematical chemistry. It discusses upper bounds, extremal graphs, and properties related to this index. The analysis includes detailed proofs, lemmas, and corollaries to characterize extremal chemical graphs of various orders and sizes.
Stats
AG(G) = 2n + 5m / 6
AG(G) = 3√2 - 13 / 6
AG(G) = 21√3 - 37 / 12
UBn,m = Upper Bound for AG(G)
Exceptions: AG(Hn,m) < UBn,m
Largest Difference: 1/2
Smallest Difference: ~0.0384