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Eccentric connectivity index and eccentric distance sum of some graph operations | ||
Transactions on Combinatorics | ||
مقاله 3، دوره 2، شماره 1، خرداد 2013، صفحه 103-111 اصل مقاله (453.49 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/toc.2013.2839 | ||
نویسندگان | ||
Buzohragul Eskender1؛ Elkin Vumar* 2 | ||
1College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, P.R. China | ||
2College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China | ||
چکیده | ||
Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of $G$, $\xi^{c}(G)$, is defined as $\xi^{c}(G)=\sum_{v\in V(G)}deg(v)ec(v)$, 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 $\xi^{d}(G)=\sum_{v\in V(G)}ec(v)D(v)$, where $D(v)=\sum_{u\in V(G)}d(u,v)$. In this paper, we calculate the eccentric connectivity index and eccentric distance sum of generalized hierarchical product of graphs. Moreover, we present the exact formulae for the eccentric connectivity index of $F$-sum graphs in terms of some invariants of the factors. | ||
کلیدواژهها | ||
Eccentric connectivity index؛ eccentric distance sum؛ generalized hierarchical product؛ $F$-sum graphs | ||
مراجع | ||
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