2016/02/11 by Milica Milivojevic, Milivojevic, Milica, Ljiljana Pavlović +1
Chemistry · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Metal-Organic Frameworks: Synthesis and Applications #Synthesis and Properties of Aromatic Compounds
paper · pdf · doi:10.48550/arxiv.1602.03698
openalex publication_date 2016/02/11 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
The variation of the Randi 'c index R'(G) of a graph G is defined by \nR(G) = \∑uv \∈ E(G) frac 1\max d(u) d(v) , where d(u) is the\ndegree of vertex u and the summation extends over all edges uv of G. Let\nG(k,n) be the set of connected simple n-vertex graphs with minimum vertex\ndegree k. In this paper we found in G(k,n) graphs for which the variation\nof the Randi 'c index attains its minimum value.\n When k \≤ frac n2 the extremal graphs are complete split graphs\nKk,n-k^*, which only vertices of two degrees, i.e. degree k and degree\nn-1, and the number of vertices of degree k is n-k, while the number of\nvertices of degree n-1 is k. For k \≥ frac n2 the extremal graphs have\nalso vertices of two degrees k and n-1, and the number of vertices of\ndegree k is frac n2. Further, we generalized results for graphs with given\nmaximum degree.\n