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https://scidar.kg.ac.rs/handle/123456789/8853
Назив: | The variation of the Randić index with regard to minimum and maximum degree |
Аутори: | Milivojević M. Pavlović, Ljiljana |
Датум издавања: | 2017 |
Сажетак: | © 2016 Elsevier B.V. The variation of the Randić index R′(G) of a graph G is defined by R′(G)=∑uv∈E(G)[formula presented], where d(u) is the degree of vertex u and the summation extends over all edges uv of G. Let G(k,n) be the set of connected simple n-vertex graphs with minimum vertex degree k. In this paper we found in G(k,n) graphs for which the variation of the Randić index attains its minimum value. When k≤[formula presented] the extremal graphs are complete split graphs Kk,n−k∗, which have only vertices of two degrees, i.e. degree k and degree n−1, and the number of vertices of degree k is n−k, while the number of vertices of degree n−1 is k. For k≥[formula presented] the extremal graphs have also vertices of two degrees k and n−1, and the number of vertices of degree k is [formula presented]. Further, we generalized results for graphs with given maximum degree. |
URI: | https://scidar.kg.ac.rs/handle/123456789/8853 |
Тип: | article |
DOI: | 10.1016/j.dam.2016.09.010 |
ISSN: | 0166-218X |
SCOPUS: | 2-s2.0-84996521019 |
Налази се у колекцијама: | Faculty of Science, Kragujevac |
Датотеке у овој ставци:
Датотека | Опис | Величина | Формат | |
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10.1016-j.dam.2016.09.010.pdf | 130.83 kB | Adobe PDF | Погледајте |
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