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The centrality of vertices has been a key issue in network analysis. For unweighted networks where edges are just present or absent and have no weight attached, many centrality measures have been presented, such as degree, betweenness, closeness, eigenvector and subgraph centrality. There has been a growing need to design centrality measures for weighted(More)
A subset of vertices of a graph G is called a feedback vertex set of G if its removal results in an acyclic subgraph. Let f (d, n) denote the minimum cardinality over all feedback vertex sets of the de Bruijn digraph B(d, n). This paper proves that for any integers d ≥ 2 and n ≥ 2 f (d, n) =  1 n ∑ i|n diφ (n i ) for 2 ≤ n ≤ 4; dn n + O(ndn−4) for n ≥(More)
Tutte observed that every nowhere-zero k-flow on a plane graph gives rise to a kvertex-coloring of its dual, and vice versa. Thus nowhere-zero integer flow and graph coloring can be viewed as dual concepts. Jaeger further shows that if a graph G has a face-k-colorable 2-cell embedding in some orientable surface, then it has a nowhere-zero k-flow. However,(More)
A subset of vertices (resp. arcs) of a graph G is called a feedback vertex (resp. arc) set of G if its removal results in an acyclic subgraph. Let f (d, n) (fa(d, n)) denote the minimum cardinality over all feedback vertex (resp. arc) sets of the Kautz digraph K(d, n). This paper proves that for any integers d 2 and n 1 f (d, n)= ⎪⎪⎪⎨ ⎪⎪⎪⎩ d for n= 1, ((More)
Underwater acoustic (UWA) communications are major tools for wireless data transmission in underwater environment. In recent years, multicarrier modulation has become one of the dominating methods in mitigating the time-delay and Doppler doubly-spread UWA acoustic channel. In this paper, one of the multicarrier modulations called filtered multitone (FMT) is(More)