A theorem on Wiener-type invariants for isometric subgraphs of hypercubesKlavžar, Sandi (Avtor) Gutman, Ivan (Avtor) mathematicsgraph theorygraph distancehypercubepartial cubeWiener numberhyper-Wiener indeksLet ▫$d(G,k)$▫ be the number of pairs of vertices of a graph ▫$G$▫ that are at distance ▫$k$▫, ▫$lambda$▫ a real (or complex) number, and ▫$W_lambda(G) = sum_{k ge 1}d(G,k)k^lambda$▫. It is proved that for a partial cube ▫$G$▫, ▫$W_{lambda + 1}(G) = |mathcal{F}| W_lambda(G) - sum_{mathnormal{F} in mathcal{F}} W_lambda(G setminus F)$▫ where ▫$mathcal{F}$▫ is the partition of ▫$E(G)$▫ induced by the Djokovic-Winkler relation ▫$Theta$▫. This result extends a previously known result for trees and implies several relations for distance-based topological indices.Elsevier20062015-07-10 14:54:46Znanstveno delo51558sl