منابع مشابه
The eccentric-distance sum of some graphs
Let G = (V,E) be a simple connected graph. The eccentric-distance sum of G is defined as ξ(G) = ∑ {u,v}⊆V (G) [e(u) + e(v)]d(u, v), where e(u) is the eccentricity of the vertex u in G and d(u, v) is the distance between u and v. In this paper, we establish formulae to calculate the eccentric-distance sum for some graphs, namely wheel, star, broom, lollipop, double star, friendship, multi-star g...
متن کاملOn the Adjacent Eccentric Distance Sum Index of Graphs
For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as [Formula in text], where [Formula in text] is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as i...
متن کاملFurther results on the eccentric distance sum
The eccentric distance sum (EDS) is a novel graph invariant which can be used to predict biological and physical properties, and has a vast potential in structure activity/property relationships. For a connected graph G, its EDS is defined as ξ d (G) = ∑ v∈V (G) ecc G (v)D G (v), where ecc G (v) is the eccentricity of a vertex v in G and D G (v) is the sum of distances of all vertices in G from...
متن کاملBounds for the Adjacent Eccentric Distance Sum
The adjacent eccentric distance sum index of a graph G is defined as ξsv(G) = ∑ v∈V (G) ε(v)D(v) deg(v) , where ε(v), deg(v) denote the eccentricity, the degree of the vertex v, respectively, and D(v) = ∑ u∈V (G) d(u, v) is the sum of all distances from the vertex v. In this paper we derive some upper or lower bounds for the adjacent eccentric distance sum in terms of some graph invariants or t...
متن کاملExtremal values on the eccentric distance sum of trees
Abstract: Let G = (VG, EG) be a simple connected graph. The eccentric distance sum of G is defined as ξ(G) = ∑ v∈VG εG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v) = ∑ u∈VG dG(u, v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-...
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: Journal of Mathematical Analysis and Applications
سال: 2011
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2011.02.086