Results 61 to 70 of about 1,125,006 (161)
Computing Analysis of Zagreb Indices for Generalized Sum Graphs under Strong Product
Journal of Chemistry, 2021 Numerous studies based on mathematical models and tools indicate that there is a strong inherent relationship between the chemical properties of the chemical compounds and drugs with their molecular structures.
Muhammad Javaid +3 more
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Independent strong domination in complementary prisms
Electronic Journal of Graph Theory and Applications, 2020 Let G = (V, E) be a graph and u,v ∈ V. Then, u strongly dominates v if (i) uv ∈ E and (ii) deg(u) ≥ deg(v). A set D ⊂ V is a strong-dominating set of G if every vertex in V-D is strongly dominated by at least one vertex in D.
Zeynep Nihan Berberler +1 more
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The geodetic domination number for the product of graphs [PDF]
Transactions on Combinatorics, 2014 A subset S of vertices in a graph G is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A subset D of vertices in G is called dominating set if every vertex not in D has at least one neighbor in D.
S. Robinson Chellathurai +1 more
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Closed Formulae for the Strong Metric Dimension of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2016 Given a connected graph G, 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. A set S of vertices is a strong metric generator for G if every pair
Kuziak Dorota +2 more
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On global (strong) defensive alliances in some product graphs
Communications in Combinatorics and Optimization, 2017 A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one more neighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The
Ismael Gonz\'alez Yero +2 more
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Journal of Functional Analysis, 1978 AbstractProduct integration is defined for a very general class of bounded-operator-valued functions on a Banach space X. Previous assumptions of continuity or Riemann-integrability of such functions are not needed. Properties of the product integral in the new setting are derived, including material on improper product integration.
Dollard, John D, Friedman, Charles N
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Bounding the Open k-Monopoly Number of Strong Product Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ {1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋} be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if δM(v)≥δG(v)2+k$\delta _M (v) \ge {{\delta _G (v)}
Kuziak Dorota +2 more
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A Sharp Lower Bound For The Generalized 3-Edge-Connectivity Of Strong Product Graphs
Discussiones Mathematicae Graph Theory, 2017 The generalized k-connectivity κk(G) of a graph G, mentioned by Hager in 1985, is a natural generalization of the path-version of the classical connectivity. As a natural counterpart of this concept, Li et al.
Sun Yuefang
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Bootstrap Percolation in Strong Products of Graphs
The Electronic Journal of CombinatoricsGiven a graph $G$ and assuming that some vertices of $G$ are infected, the $r$-neighbor bootstrap percolation rule makes an uninfected vertex $v$ infected if $v$ has at least $r$ infected neighbors. The $r$-percolation number, $m(G,r)$, of $G$ is the minimum cardinality of a set of initially infected vertices in $G$ such that after continuously ...
Bostjan Bresar, Jaka Hedzet
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Products of Extra Strong Świa̧tkowski Functions
Real Analysis Exchange, 2013 For a real-valued function \(f\) defined on a non-degenerate interval \(I\), let \({\mathcal C}(f)\) denote the set of points of continuity of \(f\). Then \(f\) is called a strong Świątkowski function if for all \(\alpha,\beta\in I\) and \(y \in (f(\alpha),f(\beta))\) there is an \(x_0\in (\alpha,\beta) \cap {\mathcal C}(f)\) such that \(f(x_0)=y ...
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