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Sufficient conditions on the zeroth-order general Randic index for maximally edge-connected digraphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 1، شماره 1، شهریور 2016، صفحه 1-13 اصل مقاله (401.82 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13514 | ||
| نویسنده | ||
| Lutz Volkmann* | ||
| RWTH Aachen University | ||
| چکیده | ||
| Let $D$ be a finite and simple digraph with vertex set $V(D)$. For a vertex $v\in V(D)$, the degree of $v$, denoted by $d(v)$, is defined as the minimum value of its out-degree $d^+(v)$ and its in-degree $d^-(v)$. Now let $D$ be a digraph with minimum degree $\delta\ge 1$ and edge-connectivity $\lambda$. If $\alpha$ is real number, then, analogously to graphs, we define the zeroth-order general Randi'{c} index by $\sum_{x\in V(D)}(d(x))^{\alpha}$. A digraph is maximally edge-connected if $\lambda=\delta$. In this paper, we present sufficient conditions for digraphs to be maximally edge-connected in terms of the zeroth-order general Randi'{c} index, the order and the minimum degree when $\alpha <0$, $0<\alpha <1$ or $1<\alpha\le 2$. Using the associated digraph of a graph, we show that our results include some corresponding known results on graphs. | ||
| کلیدواژهها | ||
| Digraphs؛ edge-connectivity؛ Maximally edge-connected digraphs؛ Zeroth-order general Randic index | ||
| مراجع | ||
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