Results 11 to 20 of about 99 (84)
On the planarity of line Mycielskian graph of a graph [PDF]
Ratio Mathematica, 2020 The line Mycielskian graph of a graph G, denoted by Lμ(G) is defined as the graph obtained from L(G) by adding q+1 new vertices E' = ei' : 1 ≤ i ≤ q and e, then for 1 ≤ i ≤ q , joining ei' to the neighbours of ei and to e.
Keerthi G. Mirajkar +1 more
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On the p3-hull number of kneser graphs [PDF]
, 2021 This paper considers an infection spreading in a graph; a vertex gets infected if at least two of its neighbors are infected. The P3-hull number is the minimum size of a vertex set that eventually infects the whole graph.
Torres, Pablo Daniel +9 more
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Period collapse in Ehrhart quasi-polynomials of \(\{1,3\}\)-graphs [PDF]
, 2022 A graph whose nodes have degree \(1\) or \(3\) is called a \(\{1,3\}\)-graph. Liu and Osserman associated a polytope to each \(\{1,3\}\)-graph and studied the Ehrhart quasi-polynomials of these polytopes.
de Pina, José +5 more
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General Randić indices of a graph and its line graph
Open Mathematics, 2023 For a real number α\alpha , the general Randić index of a graph GG, denoted by Rα(G){R}_{\alpha }\left(G), is defined as the sum of (d(u)d(v))α{\left(d\left(u)d\left(v))}^{\alpha } for all edges uvuv of GG, where d(u)d\left(u) denotes the degree of a ...
Liang Yan, Wu Baoyindureng
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On Generalized Sierpiński Graphs
Discussiones Mathematicae Graph Theory, 2017 In this paper we obtain closed formulae for several parameters of generalized Sierpiński graphs S(G, t) in terms of parameters of the base graph G. In particular, we focus on the chromatic, vertex cover, clique and domination numbers.
Rodríguez-Velázquez Juan Alberto +2 more
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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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3-Tuple Total Domination Number of Rook’s Graphs
Discussiones Mathematicae Graph Theory, 2022 A k-tuple total dominating set (kTDS) of a graph G is a set S of vertices in which every vertex in G is adjacent to at least k vertices in S. The minimum size of a kTDS is called the k-tuple total dominating number and it is denoted by γ×k,t(G).
Pahlavsay Behnaz +2 more
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Protection of Lexicographic Product Graphs
Discussiones Mathematicae Graph Theory, 2022 In this paper, we study the weak Roman domination number and the secure domination number of lexicographic product graphs. In particular, we show that these two parameters coincide for almost all lexicographic product graphs. Furthermore, we obtain tight
Klein Douglas J. +1 more
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The general position problem and strong resolving graphs
Open Mathematics, 2019 The general position number gp(G) of a connected graph G is the cardinality of a largest set S of vertices such that no three pairwise distinct vertices from S lie on a common geodesic.
Klavžar Sandi, Yero Ismael G.
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Graph Exponentiation and Neighborhood Reconstruction
Discussiones Mathematicae Graph Theory, 2021 Any graph G admits a neighborhood multiset 𝒩(G) = {NG(x) | x ∈ V (G)} whose elements are precisely the open neighborhoods of G. We say G is neighborhood reconstructible if it can be reconstructed from 𝒩(G), that is, if G ≅ H whenever 𝒩 (G) = 𝒩(H) for ...
Hammack Richard H.
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