Weak-vertex-pancyclicity of (n, k)-star graphs
نویسندگان
چکیده
منابع مشابه
(n-3)-edge-fault-tolerant Weak-pancyclicity of (n, K)-star Graphs
The (n, k)-star graph is a generalized version of the n-star graph, which belongs to the class of Cayley graphs, and has been recognized as an attractive alternative to an n-cube for building massively parallel computers. Recently, Chen et al. showed that an (n, k)-star graph is 6-weak-vertex-pancyclic for k < n–1, that is, each vertex of an (n, k)-star graph is contained in a cycle of length r...
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This work develops a novel general routing algorithm, which is a routing function, for constructing a container of width n 1 between any pair of vertices in an (n, k)-star graph with connectivity n 1. Since the wide diameters in an (n, n 1)-star graph and an (n, 1)-star graph have been derived by Lin et al. (2004), this work only addresses an (n, k)-star with 2 k n 2. The length of the longest ...
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Let $kge 1$ be an integer, and let $G$ be a finite and simple graph with vertex set $V(G)$.A weak signed Roman $k$-dominating function (WSRkDF) on a graph $G$ is a function$f:V(G)rightarrow{-1,1,2}$ satisfying the conditions that $sum_{xin N[v]}f(x)ge k$ for eachvertex $vin V(G)$, where $N[v]$ is the closed neighborhood of $v$. The weight of a WSRkDF $f$ is$w(f)=sum_{vin V(G)}f(v)$. The weak si...
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An (n, k)-star graph (Sn,k) refers to a generalized version of an n-star graph (Sn), where Sn,n−1 and Sn are isomorphic and Sn,1 is obviously a complete graph of n vertices (Kn). Since Lin et al. (2004) already calculated the wide diameters in (n, n−1)-star and (n, 1)-star graphs, this study only considers an Sn,k with 2≤k≤n−2. Lin et al. (2008) also computed upper and lower bounds of the wide ...
متن کاملRouting in Unidirectional (n, k)-star graphs
The class of (n, k)-star graphs and their unidirectional version were introduced as generalizations of star graphs and unidirectional star graphs respectively. In this paper, we substantially improved previously known bound for the the diameter of unidirectional (n, k)-star graphs. The previous bound was 10k−5 for small k and 5k+5b(n−1)/2c for large k; the new bound is 7(k−3)+18. In addition, a...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.01.035