和连通指数和色数的一个关系

A relation between sum-connectivity index and chromatic number

目的研究简单图的和连通指数和色数的一个关系。方法对和连通指数删除一个最小度点的作用。结果与结论设图G的和连通指数为X(G),v是G中最小度的点,G-v是G中删除点v后得到的图,可证得结论 X(G)≥X(G-v)并且得到和连通指数X(G)和色数χ(G)的一个关系χ(G)≤2 X(G)。

Purposes--To investigate a relation between sum-connectivity index and chromatic num- ber of a simple graph. Methods--The effect of removal of a minimum degree vertex on the sum-con- nectivity index and contradiction are employed to explore the aforesaid objective. Results and Conclu- sion-Let G be a simple graph with the sum-connectivity index X（G）, v be a vertex of G with the min- imum degree, and G≤ w the graph obtained from G by deleting v The result X≥ （G） X（G-- w） is proved, and a relationX（G） 42 X（G）between the sum-connectivity index X（G）and chromatic number is gained.