All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 46

Showing per page

The Laplacian spectrum of some digraphs obtained from the wheel

Li Su, Hong-Hai Li, Liu-Rong Zheng (2012)

Discussiones Mathematicae Graph Theory

The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.

The niche graphs of interval orders

Jeongmi Park, Yoshio Sano (2014)

Discussiones Mathematicae Graph Theory

The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if and only if...

The P 0 -matrix completion problem.

Choi, Ji Young, DeAlba, Luz Maria, Hogben, Leslie, Maxwell, Mandi S., Wangsness, Amy (2002)

ELA. The Electronic Journal of Linear Algebra [electronic only]

The Phylogeny Graphs of Doubly Partial Orders

Boram Park, Yoshio Sano (2013)

Discussiones Mathematicae Graph Theory

The competition graph of a doubly partial order is known to be an interval graph. The CCE graph and the niche graph of a doubly partial order are also known to be interval graphs if the graphs do not contain a cycle of length four and three as an induced subgraph, respectively. Phylogeny graphs are variant of competition graphs. The phylogeny graph P(D) of a digraph D is the (simple undirected) graph defined by V (P(D)) := V (D) and E(P(D)) := {xy | N+D (x) ∩ N+D(y) ¹ ⊘ } ⋃ {xy | (x,y) ∈ A(D)},...

The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Yan Ling Shao, Yubin Gao (2014)

Czechoslovak Mathematical Journal

The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A k ( A T ) k = J , where A T denotes the transpose of A and J denotes the n × n all ones matrix. For an m × n Boolean matrix M , its Boolean rank b ( M ) is the smallest positive integer b such that M = A B for some m × b Boolean matrix A and b × n Boolean matrix B . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n × n primitive matrix M in terms of its Boolean rank b ( M ) , and they also characterized all primitive...

The structure of digraphs associated with the congruence x k ≡ y ( mod n )

Lawrence Somer, Michal Křížek (2011)

Czechoslovak Mathematical Journal

We assign to each pair of positive integers n and k ≥ 2 a digraph G ( n , k ) whose set of vertices is H = { 0 , 1 , ⋯ , n - 1 } and for which there is a directed edge from a ∈ H to b ∈ H if a k ≡ b ( mod n ) . We investigate the structure of G ( n , k ) . In particular, upper bounds are given for the longest cycle in G ( n , k ) . We find subdigraphs of G ( n , k ) , called fundamental constituents of G ( n , k ) , for which all trees attached to cycle vertices are isomorphic.

Currently displaying 21 – 40 of 46