Solution to the minimum harmonic index of graphs with given minimum degree
عنوان مقاله: Solution to the minimum harmonic index of graphs with given minimum degree
شناسه ملی مقاله: JR_COMB-7-2_003
منتشر شده در در سال 1397
شناسه ملی مقاله: JR_COMB-7-2_003
منتشر شده در در سال 1397
مشخصات نویسندگان مقاله:
Meili Liang - Guangdong University of Foreign Studies
Bo Cheng - Guangdong University of Foreign Studies
Jianxi Liu - Guangdong University of Foreign Studies
خلاصه مقاله:
Meili Liang - Guangdong University of Foreign Studies
Bo Cheng - Guangdong University of Foreign Studies
Jianxi Liu - Guangdong University of Foreign Studies
The harmonic index of a graph G is defined as H(G)=\sum\limits_{uv\in E(G)}\frac{۲}{d(u)+d(v)}, where d(u) denotes the degree of a vertex u in G. Let \mathcal{G}(n,k) be the set of simple n-vertex graphs with minimum degree at least k. In this work we consider the problem of determining the minimum value of the harmonic index and the corresponding extremal graphs among \mathcal{G}(n,k). We solve the problem for each integer k (۱\le k\le n/۲) and show the corresponding extremal graph is the complete split graph K_{k,n-k}^*. This result together with our previous result which solve the problem for each integer k (n/۲ \le k\le n-۱) give a complete solution of the problem.
کلمات کلیدی: harmonic index, minimum degree, extremal graphs
صفحه اختصاصی مقاله و دریافت فایل کامل: https://civilica.com/doc/1307319/