On Eccentric Connectivity Index and Polynomial of Thorn Graph
نویسندگان
چکیده
منابع مشابه
On Eccentric Connectivity Index and Polynomial of Thorn Graph
The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized expressions for the eccentric connectivity index and polynomial of the thorn graphs, and then consider some particular cases.
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The augmented eccentric connectivity index is defined as the summation of the quotients of the product of adjacent vertex degrees and eccentricity of the concerned vertex of a graph which is a generalization of eccentric connectivity index. In this paper we present explicit expressions for the values of augmented eccentric connectivity indices of some particular thorn graphs like thorn path, th...
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let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...
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If G is a connected graph with vertex set V , then the eccentric connectivity of G, ξ C (G), is defined as v∈V deg(v) ec(v) where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. We obtain an exact lower bound on ξ C (G) in terms of order, and show that this bound is satisfied by the star graph. An asymptotically sharp upper bound is also derived. In addition, for trees of give...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2012
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2012.38139