Results 21 to 30 of about 549,593 (301)
Hamilton cycles in strong products of graphs
Journal of Graph Theory, 2005 AbstractWe prove that the strong product of any n connected graphs of maximum degree at most n contains a Hamilton cycle. In particular, GΔ(G) is hamiltonian for each connected graph G, which answers in affirmative a conjecture of Bermond, Germa, and Heydemann. © 2005 Wiley Periodicals, Inc.
Daniel Král͏̌ +3 more
openalex +4 more sources
Observations on the Lovász θ-Function, Graph Capacity, Eigenvalues, and Strong Products
Entropy, 2023 This paper provides new observations on the Lovász θ-function of graphs. These include a simple closed-form expression of that function for all strongly regular graphs, together with upper and lower bounds on that function for all regular graphs.
Igal Sason
doaj +2 more sources
On the strong metric dimension of the strong products of graphs
Open Mathematics, 2015 Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u.
Kuziak Dorota +2 more
doaj +3 more sources
Intervals and Convex Sets in Strong Product of Graphs
Graphs and Combinatorics, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iztok Peterin
openalex +5 more sources
The Geodetic Parameters of Strong Product Graphs
International Journal of Computer Applications, 2014 A set S V (G) is a split geodetic set of G, if S is a geodetic set andhV Si is disconnected. The split geodetic number of a graph G, is denoted by gs(G), is the minimum cardinality of a split geodetic set of G. A set S V (G) is a strong split geodetic set of G, if S is a geodetic set andhV Si is totally disconnected. The strong split geodetic number of
Ashalatha K.S +2 more
openalex +2 more sources
Connectivity of Strong Products of Graphs [PDF]
Graphs and Combinatorics, 2010 The strong product of graphs is one of the three commutative and associative graph products. Let \(S\) be the strong product of two given graphs. The author proves that every minimum separating set in \(S\) is either an \(I\)-set or an \(L\)-set in \(S\).
Ladinek, Irena Hrastnik, Spacapan, Simon
openaire +6 more sources
Strong Edge Coloring of Cayley Graphs and Some Product Graphs [PDF]
Graphs and Combinatorics, 2022 AbstractA strong edge coloring of a graph G is a proper edge coloring of G such that every color class is an induced matching. The minimum number of colors required is termed the strong chromatic index. In this paper we determine the exact value of the strong chromatic index of all unitary Cayley graphs.
Suresh Dara +3 more
openaire +2 more sources
Operations on Neutrosophic Vague Soft Graphs [PDF]
Neutrosophic Sets and Systems, 2022 This article concerns with the neutrosophic vague soft graphs for treating neutrosophic vague soft information by employing the theory of neutrosophic vague soft sets with graphs.
S. Satham Hussain +3 more
doaj +1 more source
Zero-sum flow number of categorical and strong product of graphs [PDF]
Transactions on Combinatorics, 2020 A zero-sum flow is an assignment of nonzero integers to the edges such that the sum of the values of all edges incident with each vertex is zero, and we call it a zero-sum $k$-flow if the absolute values of edges are less than $k$. We define the zero-sum
Muhammad Aamer Rashid +4 more
doaj +1 more source
The hull number of strong product graphs
Discussiones Mathematicae Graph Theory, 2011 A. P. Santhakumaran, Ullas Chandran S.V.
openalex +3 more sources