Results 11 to 20 of about 9,781,779 (300)
Relating the independence number and the dissociation number
Journal of Graph Theory, 2023 AbstractThe independence number and the dissociation number of a graph are the largest orders of induced subgraphs of of maximum degree at most 0 and at most 1, respectively. We consider possible improvements of the obvious inequality . For connected cubic graphs distinct from , we show , and describe the rich and interesting structure of the ...
Felix Bock +3 more
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Independent [1,2]-number versus independent domination number [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2017 Abstract A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every graph. In this paper we provide local conditions, depending on the degree of
Aleid, Sahar A. +2 more
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New Bounds for the α-Indices of Graphs
Mathematics, 2020 Let G be a graph, for any real 0≤α≤1, Nikiforov defines the matrix Aα(G) as Aα(G)=αD(G)+(1−α)A(G), where A(G) and D(G) are the adjacency matrix and diagonal matrix of degrees of the vertices of G.
Eber Lenes +2 more
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Matching Number, Independence Number, and Covering Vertex Number of Γ(Zn)
Mathematics, 2019 Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are ...
Eman AbuHijleh +3 more
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A generalization of the independence number
Discrete Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the independence numbers of a matroid
Journal of Combinatorial Theory, Series B, 1989 Given a finite subset E of a vector space of dimension 4. The number of k-independent subsets of E will be denoted by \(I_ k\). We prove that k \(I^ 2_ k\geq (k+1)I_{k-1}I_{k+1}+I_{k-1}I_ k\). The equality holds if and only if all 4-subsets of E are independent. We prove this relation for matroids of rank 4. In particular we prove Mason's conjecture on
Yahya Ould Hamidoune, Isabelle Salaün
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Shor’s bounds for the weighted independence number
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2019 Application of a technique of dual Lagrangian quadratic bounds of N.Z. Shor to studying the Maximum Weighted Independent Set problem is described. By the technique, two such N.Z. Shor’s upper bounds are obtained.
П. І. Стецюк +1 more
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On the k-Component Independence Number of a Tree
Discrete Dynamics in Nature and Society, 2021 Let G be a graph and k≥1 be an integer. A subset S of vertices in a graph G is called a k-component independent set of G if each component of GS has order at most k.
Shuting Cheng, Baoyindureng Wu
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On the Independence Number of Cayley Digraphs of Clifford Semigroups
Mathematics, 2023 Let S be a Clifford semigroup and A a subset of S. We write Cay(S,A) for the Cayley digraph of a Clifford semigroup S relative to A. The (weak, path, weak path) independence number of a graph is the maximum cardinality of an (weakly, path, weakly path ...
Krittawit Limkul, Sayan Panma
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Further Results on Packing Related Parameters in Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets
Mojdeh Doost Ali +2 more
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