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Difference labelling of cacti

Martin Sonntag (2003)

Discussiones Mathematicae Graph Theory

A graph G is a difference graph iff there exists S ⊂ IN⁺ such that G is isomorphic to the graph DG(S) = (V,E), where V = S and E = i,j:i,j ∈ V ∧ |i-j| ∈ V. It is known that trees, cycles, complete graphs, the complete bipartite graphs K n , n and K n , n - 1 , pyramids and n-sided prisms (n ≥ 4) are difference graphs (cf. [4]). Giving a special labelling algorithm, we prove that cacti with a girth of at least 6 are difference graphs, too.

Difference labelling of digraphs

Martin Sonntag (2004)

Discussiones Mathematicae Graph Theory

A digraph G is a difference digraph iff there exists an S ⊂ N⁺ such that G is isomorphic to the digraph DD(S) = (V,A), where V = S and A = {(i,j):i,j ∈ V ∧ i-j ∈ V}.For some classes of digraphs, e.g. alternating trees, oriented cycles, tournaments etc., it is known, under which conditions these digraphs are difference digraphs (cf. [5]). We generalize the so-called source-join (a construction principle to obtain a new difference digraph from two given ones (cf. [5])) and construct a difference labelling...

Differential equations forp,q-Touchard polynomials

Taekyun Kim, Orli Herscovici, Toufik Mansour, Seog-Hoon Rim (2016)

Open Mathematics

In this paper, we present differential equation for the generating function of the p, q-Touchard polynomials. An application to ordered partitions of a set is investigated.

Digital search trees and chaos game representation*

Peggy Cénac, Brigitte Chauvin, Stéphane Ginouillac, Nicolas Pouyanne (2009)

ESAIM: Probability and Statistics

In this paper, we consider a possible representation of a DNA sequence in a quaternary tree, in which one can visualize repetitions of subwords (seen as suffixes of subsequences). The CGR-tree turns a sequence of letters into a Digital Search Tree (DST), obtained from the suffixes of the reversed sequence. Several results are known concerning the height, the insertion depth for DST built from independent successive random sequences having the same distribution. Here the successive inserted words...

Digraphs are 2-weight choosable.

Khatirinejad, Mahdad, Naserasr, Reza, Newman, Mike, Seamone, Ben, Stevens, Brett (2011)

The Electronic Journal of Combinatorics [electronic only]

Digraphs contractible onto * K 3

Stefan Janaqi, François Lescure, M. Maamoun, Henry Meyniel (1998)

Mathematica Bohemica

We show that any digraph on n 3 vertices and with not less than 3 n - 3 arcs is contractible onto * K 3 .

Digraphs with isomorphic underlying and domination graphs: connected U G c ( d )

Kim A.S. Factor, Larry J. Langley (2007)

Discussiones Mathematicae Graph Theory

The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.

Currently displaying 161 – 180 of 358