Results 21 to 30 of about 101,128 (285)
Roman domination in direct product graphs and rooted product graphs [PDF]
AIMS Mathematics, 2021 <abstract><p>Let $ G $ be a graph with vertex set $ V(G) $. A function $ f:V(G)\rightarrow \{0, 1, 2\} $ is a Roman dominating function on $ G $ if every vertex $ v\in V(G) $ for which $ f(v) = 0 $ is adjacent to at least one vertex $ u\in V(G) $ such that $ f(u) = 2 $. The Roman domination number of $ G $ is the minimum weight $ \omega(f) =
Cabrera Martínez, Abel +2 more
openaire +8 more sources
Dominating the Direct Product of Two Graphs through Total Roman Strategies
Mathematics, 2020 Given a graph G without isolated vertices, a total Roman dominating function for G is a function f:V(G)→{0,1,2} such that every vertex u with f(u)=0 is adjacent to a vertex v with f(v)=2, and the set of vertices with positive labels induces a graph of ...
Abel Cabrera Martínez +3 more
doaj +3 more sources
ON PLANARITY OF DIRECT PRODUCT OF MULTIPARTITE COMPLETE GRAPHS [PDF]
Discrete Mathematics, Algorithms and Applications, 2009 The planarity of the direct product of two graphs has been widely studied in the past. Surprisingly, the missing part is the product with K2, which seems to be less predictible. In this piece of work, we characterize which subdivisions of multipartite complete graphs, have their direct product with K2 planar.
Beaudou, Laurent +3 more
openaire +5 more sources
Certain Structural Properties for the Direct Product of Cayley Graphs and Their Theoretical Applications [PDF]
Journal of MathematicsSymmetry properties are of vital importance for graphs. The famous Cayley graph is a good mathematical model as its high symmetry. The normality of the graph can well reflect the symmetry of the graph.
Li Wang, Xiaohan Ye, Weihua Yang
doaj +2 more sources
Dominating direct products of graphs [PDF]
Discrete Mathematics, 2007 Let \(G=(V,E)\) be a graph. A set \(S\subset V\) is called dominating if each vertex in \(V\backslash S\) is adjacent to at least one vertex in \(S\). The domination number \(\gamma(G)\) of a graph \(G\) is the minimum cardinality of a dominating set. For graphs \(G\) and \(H\), the direct product \(G\times H\) is the graph with vertex set \(V(G)\times
Bostjan Bresar +2 more
openaire +4 more sources
The b-chromatic index of direct product of graphs
Discrete Applied Mathematics, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Iztok Peterin, Ivo Koch
exaly +3 more sources
Resolvability and Strong Resolvability in the Direct Product of Graphs [PDF]
Results in Mathematics, 2016 Given a connected graph $G$, a vertex $w\in V(G)$ distinguishes two different vertices $u,v$ of $G$ if the distances between $w$ and $u$ and between $w$ and $v$ are different. Moreover, $w$ strongly resolves the pair $u,v$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$.
Dorota Kuziak +2 more
exaly +4 more sources
Direct product of automorphism groups of colored graphs
Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Grech
exaly +3 more sources
Direct product and uniqueness of automorphism groups of graphs
Discrete Mathematics, 1999 The author considers the problem of representing permutation groups by graphs. If \(\Aut(G)\) denotes the automorphism group of a graph \(G\) and \(A\equiv\Aut(G)\), then \(A\) is a representable permutation group. If \(A\) is represented by exactly one graph \(G\) (up to isomorphism), then \(A\) is called unique.
exaly +2 more sources
Bounds on the Twin-Width of Product Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Twin-width is a graph width parameter recently introduced by Bonnet, Kim, Thomass\'{e} & Watrigant. Given two graphs $G$ and $H$ and a graph product $\star$, we address the question: is the twin-width of $G\star H$ bounded by a function of the twin ...
William Pettersson, John Sylvester
doaj +1 more source