Further results on the eccentric distance sum
نویسندگان
چکیده
منابع مشابه
Further 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...
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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...
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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...
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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...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2012
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.10.002