Results 11 to 20 of about 78 (61)
On Accurate Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of
Cyman Joanna +2 more
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Minimally Strong Subgraph (k,ℓ)-Arc-Connected Digraphs
Discussiones Mathematicae Graph Theory, 2022 Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. A subdigraph H of D is called an S-strong subgraph if H is strong and S ⊆ V (H). Two S-strong subgraphs D1 and D2 are said to be arc-disjoint if A(D1) ∩ A(D2) = ∅.
Sun Yuefang, Jin Zemin
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
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Existence of Regular Nut Graphs for Degree at Most 11
Discussiones Mathematicae Graph Theory, 2020 A nut graph is a singular graph with one-dimensional kernel and corresponding eigenvector with no zero elements. The problem of determining the orders n for which d-regular nut graphs exist was recently posed by Gauci, Pisanski and Sciriha.
Fowler Patrick W. +4 more
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Characterizing symmetric diametrical graphs of order 12 and diameter 4
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 3, Page 145-149, 2002., 2002 A diametrical graph G is said to be symmetric if d(u,v)+d(v,u¯)=d(G) for all u, v ∈ V(G), where u¯ is the buddy of u. If moreover, G is bipartite, then it is called an S‐graph. It would be shown that the Cartesian product K2 × C6 is not only the unique S‐graph of order 12 and diameter 4, but also the unique symmetric diametrical graph of order 12 and ...
S. Al-Addasi, H. Al-Ezeh
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On Some Properties of Antipodal Partial Cubes
Discussiones Mathematicae Graph Theory, 2020 We prove that an antipodal bipartite graph is a partial cube if and only it is interval monotone. Several characterizations of the principal cycles of an antipodal partial cube are given.
Polat Norbert
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Characterizing Atoms that Result from Decomposition by Clique Separators
Discussiones Mathematicae Graph Theory, 2017 A graph is defined to be an atom if no minimal vertex separator induces a complete subgraph; thus, atoms are the graphs that are immune to clique separator decomposition.
McKee Terry A.
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Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
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Some Observations on the Smallest Adjacency Eigenvalue of a Graph
Discussiones Mathematicae Graph Theory, 2020 In this paper, we discuss various connections between the smallest eigenvalue of the adjacency matrix of a graph and its structure. There are several techniques for obtaining upper bounds on the smallest eigenvalue, and some of them are based on Rayleigh
Cioabă Sebastian M. +2 more
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On the Genus of the Co-Annihilating Graph of Commutative Rings
Discussiones Mathematicae - General Algebra and Applications, 2019 Let R be a commutative ring with identity and 𝒰R be the set of all nonzero non-units of R. The co-annihilating graph of R, denoted by 𝒞𝒜R, is a graph with vertex set 𝒰R and two vertices x and y are adjacent whenever ann(x) ∩ ann(y) = (0).
Selvakumar K., Karthik S.
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