منابع مشابه
The Randić index and the diameter of graphs
The Randić index R(G) of a graph G is defined as the sum of 1 √dudv over all edges uv of G, where du and dv are the degrees of vertices u and v, respectively. Let D(G) be the diameter of Gwhen G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path Pn achieves the minimum values for both R(G)/D(G) and R(G) − D(G). We prove this conjecture...
متن کاملOn the Higher Randić Index
Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih v v v over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...
متن کاملHermitian-Randić matrix and Hermitian-Randić energy of mixed graphs
Let M be a mixed graph and [Formula: see text] be its Hermitian-adjacency matrix. If we add a Randić weight to every edge and arc in M, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix [Formula: see text] of a mixed graph M, where [Formula: see text] ([Formula: see text]) if [Formula: ...
متن کاملOn the harmonic index of bicyclic graphs
The harmonic index of a graph $G$, denoted by $H(G)$, is defined asthe sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where$d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math. {bf 12} (2013) 716--726] proved that for any bicyclic graph $G$ of order $ngeq 4$, $H(G)le frac{n}{2}-frac{1}{15}$ and characterize all extremal bicyclic graphs.In this...
متن کاملA proof for a conjecture on the Randić index of graphs with diameter
The Randić index R(G) of a graph G is defined by R(G) = ∑ uv 1 √ d(u)d(v) , where d(u) is the degree of a vertex u in G and the summation extends over all edges uv of G. Aouchiche et al. proposed a conjecture on the relationship between the Randić index and the diameter: for any connected graph on n ≥ 3 vertices with the Randić index R(G) and the diameter D(G), R(G) − D(G) ≥ √ 2 − n+1 2 and R(G...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.08.020