Results 41 to 50 of about 124 (114)
Unordered Love in infinite directed graphs
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 4, Page 753-756, 1992., 1992 A digraph D = (V, A) has the Unordered Love Property (ULP) if any two different vertices have a unique common outneighbor. If both (V, A) and (V, A−1) have the ULP, we say that D has the SDULP. A love‐master in D is a vertex ν0 connected both ways to every other vertex, such that D − ν0 is a disjoint union of directed cycles.
Peter D. Johnson Jr.
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A Note on Roman Domination of Digraphs
Discussiones Mathematicae Graph Theory, 2019 A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S is adjacent from at least one vertex in S. The domination number of a digraph D, denoted by γ(D), is the minimum cardinality of a dominating set of D.
Chen Xiaodan, Hao Guoliang, Xie Zhihong
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The Double Roman Domatic Number of a Digraph
Discussiones Mathematicae Graph Theory, 2020 A double Roman dominating function on a digraph D with vertex set V (D) is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function f : V (D) → {0, 1, 2, 3} having the property
Volkmann Lutz
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Arc-Disjoint Hamiltonian Paths in Strong Round Decomposable Local Tournaments
Discussiones Mathematicae Graph Theory, 2021 Thomassen, [Edge-disjoint Hamiltonian paths and cycles in tournaments, J. Combin. Theory Ser. B 28 (1980) 142–163] proved that every strong tournament has a pair of arc-disjoint Hamiltonian paths with distinct initial vertices and distinct terminal ...
Meng Wei
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Notes on sufficient conditions for a graph to be Hamiltonian
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 825-827, 1991., 1990 The first part of this paper deals with an extension of Dirac′s Theorem to directed graphs. It is related to a result often referred to as the Ghouila‐Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila‐Houri Theorem is redundant. The Second part of the paper shows that a condition on the number
Michael Joseph Paul +2 more
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Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code
Discussiones Mathematicae Graph Theory, 2021 A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph
Balbuena Camino +2 more
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Traffic and Emergency Network Optimisation Using Domination in Picture Fuzzy Directed Graphs
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, the picture fuzzy digraphs PFDGs are analysed in depth concerning their domination number (DN) and connectedness, offering new insights into structural properties and decision‐making approaches for handling uncertainty. Picture fuzzy sets (PFS) are a generalisation of traditional intuitionistic fuzzy sets, which provide a mathematical ...
J. Shivangi Mishra +6 more
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A digraph equation for homomorphic images
International Journal of Mathematics and Mathematical Sciences, Volume 9, Issue 2, Page 409-411, 1986., 1986 The definitions of a homomorphism and a contraction of a graph are generalized to digraphs. Solutions are given to the graph equation .
Robert D. Girse, Richard A. Gillman
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Eulerian polynomials for digraphs [PDF]
Given an \(n\)-vertex digraph \(D\) and a labeling \(\sigma:V(D)\to [n]\), we say that an arc \(u\to v\) of \(D\) is a descent of \(\sigma\) if \(\sigma(u)›\sigma(v)\). Foata and Zeilberger introduced a generating function \(A_D(t)\) for labelings of \(D\
Celano, Kyle +2 more
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On characteristic and permanent polynomials of a matrix
Special Matrices, 2017 There is a digraph corresponding to every square matrix over ℂ. We generate a recurrence relation using the Laplace expansion to calculate the characteristic and the permanent polynomials of a square matrix.
Singh Ranveer, Bapat R. B.
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