Results 11 to 20 of about 969,174 (273)
Incidence matrices and line graphs of mixed graphs
Special Matrices, 2023 In the theory of line graphs of undirected graphs, there exists an important theorem linking the incidence matrix of the root graph to the adjacency matrix of its line graph. For directed or mixed graphs, however, there exists no analogous result.
Abudayah Mohammad +2 more
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Mixed graph colouring as scheduling multi-processor tasks with equal processing times
Журнал Белорусского государственного университета: Математика, информатика, 2021 A problem of scheduling partially ordered unit-time tasks processed on dedicated machines is formulated as a mixed graph colouring problem, i. e., as an assignment of integers (colours) {1, 2, …, t} to the vertices (tasks) V {ν1, ν2, …, νn}, of the mixed
Yuri N. Sotskov
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Integral mixed circulant graphs
Discrete Mathematics, 2023 A mixed graph is said to be \textit{integral} if all the eigenvalues of its Hermitian adjacency matrix are integer. The \textit{mixed circulant graph} $Circ(\mathbb{Z}_n,\mathcal{C})$ is a mixed graph on the vertex set $\mathbb{Z}_n$ and edge set $\{ (a,b): b-a\in \mathcal{C} \}$, where $0\not\in \mathcal{C}$.
Monu Kadyan, Bikash Bhattacharjya
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On bipartite‐mixed graphs [PDF]
Journal of Graph Theory, 2018 AbstractMixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this article, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore‐like bound is attained in the case of diameter , and that bipartite‐mixed graphs of diameter do not exist.
Dalfó Simó, Cristina +2 more
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Enumeration of Mixed Graphs [PDF]
Proceedings of the American Mathematical Society, 1966 and three oriented lines. An ordinary graph may be regarded as a mixed graph with no oriented lines, and an oriented graph as a mixed graph with no ordinary lines. Further, any digraph may be considered as a mixed graph by changing each symmetric pair of lines to an ordinary line.
Harary, Frank, Palmer, Edgar M.
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Total mixed domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2022 For a graph [Formula: see text] we call a subset [Formula: see text] a total mixed dominating set of G if each element of [Formula: see text] is either adjacent or incident to an element of S, and the total mixed domination number of G is the minimum ...
Adel P. Kazemi +2 more
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HS-integral and Eisenstein integral mixed circulant graphs
Theory and Applications of Graphs, 2023 A mixed graph is called \emph{second kind hermitian integral} (\emph{HS-integral}) if the eigenvalues of its Hermitian-adjacency matrix of the second kind are integers.
Monu Kadyan, Bikash Bhattacharjya
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Stochastic and mixed flower graphs [PDF]
Physical Review E, 2020 11 pages, 6 ...
C. Tyler Diggans +2 more
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Discrete Mathematics & Theoretical Computer Science, 2023 Mixed graphs have both directed and undirected edges. A mixed cage is a regular mixed graph of given girth with minimum possible order. In this paper mixed cages are studied. Upper bounds are obtained by general construction methods and computer searches.
Geoffrey Exoo
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Mixed Graph Colorings: A Historical Review
Mathematics, 2020 This paper presents a historical review and recent developments in mixed graph colorings in the light of scheduling problems with the makespan criterion. A mixed graph contains both a set of arcs and a set of edges. Two types of colorings of the vertices
Yuri N. Sotskov
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