76 research outputs found
On the General Sum-connectivity Index of Connected Graphs with Given Order and Girth
In this paper, we show that in the classof connected graphs of order having girth at least equal to , , the unique graph having minimum general sum-connectivity index consists of and pendant vertices adjacent to a unique vertex of , if -1\leq \alpha <0. This property does not hold for zeroth-order general Randi\' c index
General degree distance of graphs
We generalize several topological indices and introduce the general degree distance of a connected graph . For , the general degree distance , where is the vertex set of , is the degree of a vertex , and is the distance between and in . We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices
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