2021/07/09 by Zhao Wang, Wang, Zhao, Yaping Mao +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO
paper · pdf · doi:10.48550/arxiv.2107.05742
arxiv created 2021/07/09 · arxiv updated 2021/07/14
Building upon the notion of Gutman index SGut(G), Mao and Das recently introduced the Steiner Gutman index by incorporating Steiner distance for a connected graph G. The Steiner Gutman k-index SGutk(G) of G is defined by SGutk(G) =∑S⊆ V(G), |S|=k(∏v∈ SdegG(v)) dG(S), in which dG(S) is the Steiner distance of S and degG(v) is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on SGutk, and then investigate the Nordhaus-Gaddum-type results for the parameter SGutk. We obtain sharp upper and lower bounds of SGutk(G)+SGutk(G) and SGutk(G)⋅ SGutk(G) for a connected graph G of order n, m edges and maximum degree Δ, minimum degree δ.