منابع مشابه
The optimal rubbling number of ladders, prisms and Möbius-ladders
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices v and w adjacent to a vertex u, and an extra pebble is added at vertex u. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that v...
متن کاملRank numbers for bent ladders
A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices with the same label contains a vertex with a larger label. The rank number of a graph is the fewest number of labels that can be used in a ranking. The rank number of a graph is known for many families, including the ladder graph P2 × Pn. We consider how ”bending” a ladder affects ...
متن کاملFeedback numbers of Kautz digraphs
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, ( )(n) n + ( )(n− 1) n− 1 for 2 n 7, dn n +...
متن کاملFeedback numbers of Kautz undirected graphs
The feedback number f(d, n) of the Kautz undirected graph UK(d, n) is the minimum number of vertices whose removal results in an acyclic graph. This paper shows (d − dn−1 − 1 2 d(d + 1) + 1)/(2d − 1) ≤ f(d, n) ≤ d − ( d2 4 + 1)dn−2, which implies that f(2, n) = 2n−1, as obtained by Královič and Ružička [Information Processing Letters 86 (4) (2003), 191–196].
متن کاملFeedback numbers of de Bruijn digraphs
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 ≥ 5, where i | nmeans i divides n, and ...
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ژورنال
عنوان ژورنال: ITM Web of Conferences
سال: 2019
ISSN: 2271-2097
DOI: 10.1051/itmconf/20192501013