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Infinite Hamiltonian paths in Cayley digraphs [PDF]
Discrete Mathematics, 1985 Let Cay(S:H) be the Cayley digraph of the generators S in the group H. A one-way infinite Hamiltonian path in the digraph G is a listing of all the vertices \([v_ i: 1\leq ...
Jungreis, Irwin L
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Asymptotic enumeration of graphical regular representations
Proceedings of the London Mathematical Society, Volume 127, Issue 5, Page 1424-1450, November 2023., 2023 Abstract We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have full automorphism groups ‘as small as possible’. This confirms a conjecture of Babai–Godsil–Imrich–Lovász on the proportion of GRRs, as well as a conjecture of Xu on ...
Binzhou Xia, Shasha Zheng
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Minimal‐time complex consensus for multi‐agent systems with time delay
IET Control Theory &Applications, Volume 16, Issue 12, Page 1182-1193, August 2022., 2022 Abstract This paper studies the minimum time consensus problem for discrete‐time multi‐agent systems with complex Laplacian delay networks such that each agent can find its complex consensus value in a minimum number of steps using its local observations.
Chao Zou, Li Yu, Simon Yang, Linlin Ou
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Certain Concepts in Vague Graph with an Application
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 Vague graphs (VGs), belonging to the FGs family, have good capabilities when faced with problems that cannot be expressed by FGs. When an element’s membership is not clear, neutrality is a good option that can be well‐supported by a VG. The previous definition limitations in irregular‐FG have led us to offer new definitions in VGs.
Xiaolong Shi +4 more
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Mobius Group Generated by Two Elements of Order 2, 4, and Reduced Quadratic Irrational Numbers
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 The construction of circuits for the evolution of orbits and reduced quadratic irrational numbers under the action of Mobius groups have many applications like in construction of substitution box (s‐box), strong‐substitution box (s.s‐box), image processing, data encryption, in interest for security experts, and other fields of sciences.
Dilshad Alghazzawi +5 more
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[Retracted] Novel Concepts in Bipolar Fuzzy Graphs with Applications
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Many problems of practical interest can be modeled and solved by using bipolar graph algorithms. Bipolar fuzzy graph (BFG), belonging to fuzzy graphs (FGs) family, has good capabilities when facing with problems that cannot be expressed by FGs. Hence, in this paper, we introduce the notion of (ϑ, δ)−homomorphism of BFGs and classify homomorphisms (HMs),
Chang Wan +6 more
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Studies of Chordal Ring Networks via Double Metric Dimensions
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 Locating the sources of information spreading in networks including tracking down the origins of epidemics, rumors in social networks, and online computer viruses, has a wide range of applications. In many situations, identifying where an epidemic started, or which node in a network served as the source, is crucial. But it can be difficult to determine
M. Ahmad +4 more
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A Study on Interval‐Valued Fuzzy Graph with Application in Energy Industry Management
Discrete Dynamics in Nature and Society, Volume 2022, Issue 1, 2022., 2022 In this paper, we define the concept of level graphs on interval‐valued fuzzy graphs (IVFGs) and introduce the notions of [α, β]−[α, β]− homomorphism, isomorphism, weak isomorphism, and co‐weak isomorphism of IVFGs by [α, β]− homomorphism. Also, an application of homomorphism of IVFGs has been presented by using coloring‐FG.
Xiaoli Qiang +6 more
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Novel Concepts in Vague Graphs with Application in Hospital’s Management System
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 Many problems of practical interest can be modeled and solved by using vague graph (VG) algorithms. Vague graphs, belonging to the fuzzy graphs (FGs) family, have good capabilities when faced with problems that cannot be expressed by FGs. Hence, in this paper, we introduce the notion of (η, γ)‐ HMs of VGs and classify homomorphisms (HMs), weak ...
Xiaolong Shi +5 more
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European Journal of Combinatorics, 2011 Graph labeling, introduced by \textit{A. Rosa} in [``On certain valuations of the vertices of a graph,'' Theory Graphs, Int. Symp. Rome 1966, 349--355 (1967; Zbl 0193.53204)], deals with assigning integers to the vertices or edges or both satisfying some combinatorial constraint. Labeled graphs serve as useful models for numerous applications such as a
K. Thirusangu +2 more
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