Extremal Bounds for the Complementary Second Zagreb Index in Chemical Graph Theory
Partial results toward the Furtula-Oz conjecture that the connected graph on n vertices maximizing the complementary second Zagreb index cM2(G) = sum over edges uv of |deg(u)^2 - deg(v)^2| is the join of a complete graph K_k with the complement of K_{n-k} for some k below n/2. The work proves the maximizer has a vertex of degree n-1, that no two of its minimum-degree vertices are adjacent, and an explicit upper bound (roughly k < 0.535 n) on its count of maximum-degree vertices, and confirms the conjecture for certain bidegreed and tridegreed graph families.
On a Conjecture Concerning the Complementary Second Zagreb Index
A chemical-graph-theory paper on a degree-based topological index called the complementary second Zagreb index, cM2(G), which sums the absolute differences of squared endpoint degrees over all edges …