The second edge-Wiener index of some composite graphs
نویسندگان
چکیده
منابع مشابه
The Second Edge-wiener Index of Some Composite Graphs
In this paper we study the behavior of the second edge-Wiener index under the join and corona product of graphs. Results are applied for some classes of graphs such as suspensions, bottlenecks, and thorny graphs. 2010 Mathematics Subject Classification: 05C12; 05C62; 92E10
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Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In thi...
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let $g$ be a simple connected graph. the edge-wiener index $w_e(g)$ is the sum of all distances between edges in $g$, whereas the hyper edge-wiener index $ww_e(g)$ is defined as {footnotesize $w{w_e}(g) = {frac{1}{2}}{w_e}(g) + {frac{1}{2}} {w_e^{2}}(g)$}, where {footnotesize $ {w_e^{2}}(g)=sumlimits_{left{ {f,g} right}subseteq e(g)} {d_e^2(f,g)}$}. in this paper, we present explicit formula fo...
متن کاملmore on edge hyper wiener index of graphs
let $g=(v(g),e(g))$ be a simple connected graph with vertex set $v(g)$ and edge set $e(g)$. the (first) edge-hyper wiener index of the graph $g$ is defined as: $$ww_{e}(g)=sum_{{f,g}subseteq e(g)}(d_{e}(f,g|g)+d_{e}^{2}(f,g|g))=frac{1}{2}sum_{fin e(g)}(d_{e}(f|g)+d^{2}_{e}(f|g)),$$ where $d_{e}(f,g|g)$ denotes the distance between the edges $f=xy$ and $g=uv$ in $e(g)$ and $d_{e}(f|g)=s...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2014
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2014.1006