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 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 distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
متن کاملRandić index, irregularity and complex biomolecular networks.
A new formulation of Randić index is carried out as a minimization of a quadratic form which involves the Laplacian matrix of a graph. Using this formulation it is easy to realize that Randić index is useful in defining a new index of irregularity, which is then formulated here. A new context for the study of irregularity of graphs is advanced as a necessity for studying complex (biological) ne...
متن کاملAlgorithms and complexity results for finding graphs with extremal Randić index
We show that finding a subgraph realization with the minimum generalized Randić index for a given base graph and degree sequence is solvable in polynomial time by formulating the problem as the minimum weight perfect b-matching problem of Edmonds (J Res Natl Bur Stand 69B (1965), 125–130). However, the realization found via this reduction is not guaranteed to be connected. Approximating the min...
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: Rocky Mountain Journal of Mathematics
سال: 2010
ISSN: 0035-7596
DOI: 10.1216/rmj-2010-40-2-713