Results 71 to 80 of about 16,499 (231)

On the Hardness of Switching to a Small Number of Edges

Journal of Graph Theory, EarlyView.
ABSTRACT Seidel's switching is a graph operation which makes a given vertex adjacent to precisely those vertices to which it was non‐adjacent before, while keeping the rest of the graph unchanged. Two graphs are called switching‐equivalent if one can be made isomorphic to the other one by a sequence of switches. Jelínková et al. [DMTCS 13, no. 2, 2011]
Vít Jelínek, Eva Jelínková, Jan Kratochvíl   +2 more
wiley   +1 more source

Distributed Continuous-Time Convex Optimization on Weight-Balanced Digraphs [PDF]

IEEE Transactions on Automatic Control, 2012
This technical note studies the continuous-time distributed optimization of a sum of convex functions over directed graphs. Contrary to what is known in the consensus literature, where the same dynamics works for both undirected and directed scenarios ...
B. Gharesifard, J. Cortés
semanticscholar   +1 more source

A Min–Max Relation on Dicuts and Dijoins in Weighted Chordal Digraphs

Journal of Graph Theory, EarlyView.
ABSTRACT In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects every dicut. Edmonds and Giles conjectured that in a weighted digraph, the minimum weight of a dicut is equal to the maximum size of a packing of dijoins. This has been disproved. However, the unweighted version conjectured by
Gérard Cornuéjols, Siyue Liu, R. Ravi
wiley   +1 more source

Distance in Digraphs

Computers & Mathematics with Applications, 1997
The authors recall known results concerning distance in a graph and standard distance in a digraph. They define two new distances in strong digraphs: \(d_{\max} (u,v)= \max (d(u,v),\;d(v,u))\) and \(d_{\text{sum}} (u,v)= d(u,v) +d(v,u)\). Several results and problems concerning these distances and parameters such as center, median, and periphery are ...
Chartrand, G., Tian, S.
openaire   +1 more source

Digraph homomorphisms on \(Z_n\)-digraph

Malaya Journal of Matematik, 2020
A graph homomorphism is a mapping between two graphs that respect their structure. In this paper we develop some results related to digraph homomorphisms for the class of \({\overrightarrow{Z_n}}^{-}\)-digraphs. We will begin by giving some standard definitions, then expanding our focus to specifically study different types of digraph homomorphisms. In
null Jimly Manuel, null Bindhu K Thomas
openaire   +1 more source

An End Degree for Digraphs

Journal of Graph Theory, EarlyView.
ABSTRACT In this paper we define a degree for ends of infinite digraphs. The well‐definedness of our definition in particular resolves a problem by Zuther. Furthermore, we extend our notion of end degree to also respect, among others, the vertices dominating the end, which we denote as combined end degree.
Matthias Hamann, Karl Heuer
wiley   +1 more source

On the Capacity of Digraphs

European Journal of Combinatorics, 1998
For a digraph \(G= (V,E)\) let \(\omega(G^n)\) denote the maximum possible cardinality of a subset \(S\) of \(V^n\) in which for every ordered pair of \(n\)-tuples \((u_1, u_2,\dots, u_n)\) and \((v_1, v_2,\dots, v_n)\) of members of \(S\) there is some \(i\) with \(1\leq i\leq n\) such that \((u_i,v_i)\in E\). The capacity \(C(G)\) of \(G\) is \(C(G)=
openaire   +2 more sources

Dual digraphs of finite meet-distributive and modular lattices

Cubo
We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015 ...
Andrew Craig, Miroslav Haviar, Klarise Marais   +2 more
doaj   +1 more source

Hermitian Adjacency Matrix of Digraphs and Mixed Graphs [PDF]

Journal of Graph Theory, 2015
The article gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from x to y is equal to the complex unity i (and its ...
Krystal Guo, B. Mohar
semanticscholar   +1 more source

Tree Independence Number III. Thetas, Prisms and Stars

Journal of Graph Theory, EarlyView.
ABSTRACT We prove that for every t ∈ N $t\in {\mathbb{N}}$ there exists τ = τ ( t ) ∈ N $\tau =\tau (t)\in {\mathbb{N}}$ such that every (theta, prism, K 1 , t ${K}_{1,t}$)‐free graph has tree independence number at most τ $\tau $ (where we allow “prisms” to have one path of length zero).
Maria Chudnovsky, Sepehr Hajebi, Nicolas Trotignon   +2 more
wiley   +1 more source