The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman;Klein, Mihali?,, Plav?i? and Trinajsti?) is kn...The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman;Klein, Mihali?,, Plav?i? and Trinajsti?) is known regarding their correlation, that for a tree T with n vertices. In this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.展开更多
文摘The degree distance of a graph G is , where and are the degrees of vertices , and is the distance between them. The Wiener index is defined as . An elegant result (Gutman;Klein, Mihali?,, Plav?i? and Trinajsti?) is known regarding their correlation, that for a tree T with n vertices. In this note, we extend this study for more general graphs that have frequent appearances in the study of these indices. In particular, we develop a formula regarding their correlation, with an error term that is presented with explicit formula as well as sharp bounds for unicyclic graphs and cacti with given parameters.
