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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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Mixed picture fuzzy graph [PDF]
Ratio Mathematica, 2022 A new form of picture fuzzy graph has been identified and introduced here as Mixed Picture Fuzzy Graph(MPFG). The picture fuzzy set is made up of the fuzzy set and the intuitionistic fuzzy set.
K.K. Myithili, C. Nandhini
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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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The 2-colouring problem for $(m,n)$-mixed graphs with switching is polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 A mixed graph is a set of vertices together with an edge set and an arc set. An $(m,n)$-mixed graph $G$ is a mixed graph whose edges are each assigned one of $m$ colours, and whose arcs are each assigned one of $n$ colours. A \emph{switch} at a vertex $v$
Richard C Brewster +2 more
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The Spectral Distribution of Random Mixed Graphs
Axioms, 2022 In this work, we propose a random mixed graph model Gn(p(n),q(n)) that incorporates both the classical Erdős-Rényi’s random graph model and the random oriented graph model.
Yue Guan +7 more
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Identifying the Shortest Path of a Semidirected Graph and Its Application
Mathematics, 2022 The basic goal of this research is to find the shortest path of a semidirected graph and apply it to the road network system. In the field of graph theory, networks are described as directed graphs, undirected graphs, or a combination of both.
Rakhi Das +4 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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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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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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