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The Laplacian eigenvalues of mixed graphs
Linear Algebra and its Applications, 2003 The first part of the paper gives an upper bound for the second smallest Laplacian eigenvalue of the mixed graphs, thereby generalizing the results of \textit{M. Fiedler} [Czech. Math. J. 23, 298-305 (1973; Zbl 0265.05119)]. The second part presents two sharp upper bounds for the largest Laplacian eigenvalues of the mixed graphs in terms of the largest,
Rong Luo, Xiao-Dong Zhang
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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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Journal of Educational Research in Mathematics, 2020 In this study, in order to explore ways that statistical graphs teaching in elementary mathematics education can be improved, first, the types of statistical graphs that appear in middle school social textbooks were examined, and second, the ...
Byungjoo Tak, Eun-Sung Ko
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Research and Application of Hypernetwork Energy
Jisuanji kexue yu tansuo, 2021 Graph energy plays an important role in research of graph theory. Graph energy and many other similar variants have been applied in many other types of graphs, e.g., undirected graphs, oriented graphs, mixed graphs, and so on.
LIU Shengjiu, LI Tianrui, LIU Jia, XIE Peng
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Representations of Quivers and Mixed Graphs [PDF]
, 2013 This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The notion of quiver representations is extended to representations of mixed graphs, which permits one to study ...
Roger A. Horn, Vladimir V. Sergeichuk
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Best Graph Type to Compare Discrete Groups: Bar, Dot, and Tally
Frontiers in Psychology, 2021 Different graph types might differ in group comparison due to differences in underlying graph schemas. Thus, this study examined whether graph schemas are based on perceptual features (i.e., each graph has a specific schema) or common invariant ...
Fang Zhao, Robert Gaschler
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The Laplacian spectrum of a mixed graph
Linear Algebra and its Applications, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiao-Dong Zhang, Jiong-Sheng Li
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Uniform Mixing on Cayley Graphs [PDF]
The Electronic Journal of Combinatorics, 2017 We provide new examples of Cayley graphs on which the quantum walks reach uniform mixing. Our first result is a complete characterization of all $2(d+2)$-regular Cayley graphs over $\mathbb{Z}_3^d$ that admit uniform mixing at time $2\pi/9$. Our second result shows that for every integer $k\ge 3$, we can construct Cayley graphs over $\mathbb{Z}_q^d ...
Hanmeng Zhan, Chris Godsil
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Mixed Moore Cayley Graphs [PDF]
Journal of Interconnection Networks, 2017 The degree-diameter problem seeks to find the largest possible number of vertices in a graph having given diameter and given maximum degree. There has been much recent interest in the problem for mixed graphs, where we allow both undirected edges and directed arcs in the graph.
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Moore mixed graphs from Cayley graphs
Electronic Journal of Graph Theory and Applications, 2023 This research has been partially supported by AGAUR from the Catalan Government under project 2021SGR00434 and MICINN from the Spanish Government under project PID2020-115442RBI00.
Dalfó Simó, Cristina +1 more
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