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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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Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]
PLoS ONELet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma +4 more
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A note on orientations of mixed graphs [PDF]
Discrete Applied Mathematics, 2002 The authors study an orientation problem on mixed graphs. The goal is to obtain a directed graph satisfying a certain connectivity requirement. First the authors continue the study of the pair connectivity problem and show that it is NP-complete for mixed graphs. Then they prove several results for two pairs of nodes of mixed graphs.
Esther M. Arkin, Refael Hassin
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𝕮-inverse of graphs and mixed graphs
Open MathematicsThis article introduces a generalization of the concept of inverse graphs applicable to both graphs and mixed graphs. Given a graph GG with adjacency matrix A(G)A\left(G), the inverse graph G−1{G}^{-1} is defined such that its adjacency matrix is similar
Alomari Omar +2 more
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γ-Inverse graph of some mixed graphs
Special MatricesLet GG be a graph. Then, the inverse graph G−1{G}^{-1} of GG is defined to be a graph that has adjacency matrix similar to the inverse of the adjacency matrix of GG, where the similarity matrix is ±1\pm 1 diagonal matrix. In this article, we introduced a
Boulahmar Wafa +2 more
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Bernoulli, 2013 Published in at http://dx.doi.org/10.3150/12-BEJ454 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
Kayvan Sadeghi
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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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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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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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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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