Results 1 to 10 of about 356,658 (166)
Domination Number, Independent Domination Number and 2-Independence Number in Trees
Discussiones Mathematicae Graph Theory, 2021 For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees ...
Dehgardi Nasrin +4 more
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On the signed $2$-independence number of graphs [PDF]
Electronic Journal of Graph Theory and Applications, 2017 In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach.
S.M. Hosseini Moghaddam +3 more
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On Selkow’s Bound on the Independence Number of Graphs
Discussiones Mathematicae Graph Theory, 2019 For a graph G with vertex set V (G) and independence number α(G), Selkow [A Probabilistic lower bound on the independence number of graphs, Discrete Math. 132 (1994) 363–365] established the famous lower bound ∑v∈V(G)1d(v)+1(1+max{d(v)d(v)+1-∑u∈N(v)1d(u)+
Harant Jochen, Mohr Samuel
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On the strength and independence number of graphs [PDF]
Contributions to Mathematics, 2022 Rikio Ichishima +2 more
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On the number of independent orders [PDF]
Annals of Pure and Applied Logic, 2021 We investigate a model theoretic invariant $κ_{srd}^m(T)$, which was introduced by Shelah in his famous book, and prove that $κ_{srd}^m(T)$ is sub-additive. When $κ_{srd}^m(T)$ is infinite, this gives the equality $κ^m_{srd}(T)=κ^1_{srd}(T)$, answering a question by Shelah. We apply the same proof method to analyze another invariant $κ^m_{ird}(T)$, and
Kota Takeuchi, Akito Tsuboi
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On the Stability of the Graph Independence Number [PDF]
SIAM Journal on Discrete Mathematics, 2022 Let $G$ be a graph on $n$ vertices of independence number $α(G)$ such that every induced subgraph of $G$ on $n-k$ vertices has an independent set of size at least $α(G) - \ell$. What is the largest possible $α(G)$ in terms of $n$ for fixed $k$ and $\ell$? We show that $α(G) \le n/2 + C_{k, \ell}$, which is sharp for $k-\ell \le 2$.
Zichao Dong, Zhuo Wu
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Discontinuity and diversity of Persian scientific research journals in the field of educational sciences by using coloring and mathematical algebraic parameters [PDF]
ریاضی و جامعه, 2022 The aim of the current research is to study and compare graphs authorship by Iranian researchers in Persian scientific research journals in the field of educational sciences by using algebraic parameters of mathematics. In this research, the data related
Ali Abdi, Mostafa Amini
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General Properties on Differential Sets of a Graph
Axioms, 2021 Let G=(V,E) be a graph, and let β∈R. Motivated by a service coverage maximization problem with limited resources, we study the β-differential of G. The β-differential of G, denoted by ∂β(G), is defined as ∂β(G):=max{|B(S)|−β|S|suchthatS⊆V}.
Ludwin A. Basilio +3 more
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On the broadcast independence number of caterpillars [PDF]
Discrete Applied Mathematics, 2018 Let $G$ be a simple undirected graph.A broadcast on $G$ isa function $f : V(G)\rightarrow\mathbb{N}$ such that $f(v)\le e\_G(v)$ holds for every vertex $v$ of $G$, where $e\_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum distance from $v$ to any other vertex of $G$.The cost of $f$ is the value ${\rm cost}(f)=\sum\_{v\in V(G)}f(v)$.A
Messaouda Ahmane +2 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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