Results 11 to 20 of about 3,952,319 (243)
Computing Certain Topological Indices of the Line Graphs of Subdivision Graphs of Some Rooted Product Graphs [PDF]
Mathematics, 2019 In this work, we study the degree-based topological invariants, and the general sum-connectivity, A B C 4 , G A 5 , general Zagreb, G A , generalized Randić, and A B C indices of the line graphs of some rooted product ...
Adnan Aslam +4 more
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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
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Equitable Coloring On Rooted Product Of Graphs
Turkish Journal of Computer and Mathematics Education (TURCOMAT), 2021 A finite and simple graph is said to be equitably colorable if its vertices can be partitioned into classes such that each is an independent set and holds for every . The smallest integer for which is equitable chromatic number of and denoted by .
et. al., Loura Jency ,
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On the b-chromatic number of rooted product graphs [PDF]
FilomatThe b-chromatic number of a graph G was defined by Irving and Manlove in 1999 as the largest integer k for which G admits a proper coloring with k colors such that every color class (in this proper coloring) has a vertex that is adjacent to at least one vertex in every other color class.
Sarah Bockting-Conrad +2 more
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Weak Roman domination in rooted product graphs
AIMS Mathematics, 2021 In this paper, we obtain closed formulae for the weak Roman domination number of rooted product graphs. As a consequence of the study, we show that the use of rooted product graphs is a useful tool to show that the problem of computing the weak Roman domination number of a graph is NP-hard.
Rangel Hernández-Ortiz +2 more
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Roman domination in direct product graphs and rooted product graphs1
, 2021 Let G be a graph with vertex set V(G). A function f : V(G) -> {0, 1, 2) is a Roman dominating function on G if every vertex v is an element of V(G) for which f(v) = 0 is adjacent to at least one vertex u is an element of V(G) such that f(u) = 2. The Roman domination number of G is the minimum weight omega(f) = Sigma(x is an element of V(G)) f(x) among ...
Cabrera Martínez, Abel +2 more
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On the outer-independent {2}-domination in rooted product graphs
Open MathematicsLet G be a graph with vertex set V(G). A function f: V(G) → {0, 1, 2} is called an outer-independent {2}-dominating function on G if ∑ u∈N[v] f(u) ≥ 2 for every vertex v ∈ V(G) and {v ∈ V(G) : f(v) = 0} is an independent set of G. The minimum weight ω(f)
Cabrera-Martínez Abel +2 more
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Italian Domination in Rooted Product Graphs [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2020 In this article, we obtain closed formulae for the Italian domination number of rooted product graphs. As a particular case of the study, we derive the corresponding formulas for corona graphs, and we provide an alternative proof that the problem of computing the Italian domination number of a graph is NP-hard.
R. Hernández-Ortiz +2 more
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A Heuristic for Direct Product Graph Decomposition [PDF]
, 2023 In this paper we describe a heuristic for decomposing a directed graph into factors according to the direct product (also known as Kronecker, cardinal or tensor product). Given a directed, unweighted graph G with adjacency matrix Adj(G), our heuristic
Moreno Marzolla +2 more
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Spectra of M-edge rooted product of graphs
Indian Journal of Pure and Applied Mathematics, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Pavithra, R. Rajkumar
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