Abstract The status or transmission of a vertex u in a graph G is defined by σ ( u ) = ∑ v ∈ V d ( u , v ) , where V is the set of vertices of the graph G, and d ( u , v ) stands for the distance between u and v in G. In this paper we have defined inverse sum indeg status (ISIS) index of a graph G as I S I S ( G ) = ∑ u v ∈ E σ ( u ) σ ( v ) σ ( u ) + σ ( v ) , where E is the set of edges of G. The ISIS index is investigated as a predictor of various physicochemical properties of octane isomers and boiling points of benzenoid hydrocarbons. We further compute this novel index of some specific graphs and also obtain some bounds of the proposed index.

中文翻译：

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图的逆和 indeg 状态指数及其在辛烷异构体和苯类烃中的应用

摘要 图 G 中顶点 u 的状态或传递由 σ ( u ) = ∑ v ∈ V d ( u , v ) 定义，其中 V 是图 G 的顶点集，d ( u , v ) 代表 G 中 u 和 v 之间的距离。在本文中，我们将图 G 的逆和 indeg 状态 (ISIS) 索引定义为 ISIS ( G ) = ∑ uv ∈ E σ ( u ) σ ( v ) σ ( u ) + σ ( v ) ，其中 E 是 G 的边集。研究 ISIS 指数作为辛烷异构体的各种物理化学性质和苯类烃沸点的预测指标。我们进一步计算了一些特定图的这个新索引，并获得了建议索引的一些界限。