Results 11 to 20 of about 3,567 (160)
A novel characterization of cubic Hamiltonian graphs via the associated quartic graphs [PDF]
Ars Math. Contemp., 2015 We give a necessary and sufficient condition for a cubic graph to be Hamiltonian by analyzing Eulerian tours in certain spanning subgraphs of the quartic graph associated with the cubic graph by 1-factor contraction. This correspondence is most useful in
S. Bonvicini, T. Pisanski
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Mathematical Investigation of Eulerian and Hamiltonian Graphs in Complex Networks
This study investigates the properties and applications of Eulerian and Hamiltonian graphs within complex networks, with a particular focus on their roles in transportation, communication, and biological systems. The primary objective is to develop a deeper mathematical understanding of these graph structures and their implications for optimizing ...
Md Asaduzzaman
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On Hamiltonian Decomposition Problem of 3-Arc Graphs. [PDF]
Comput Intell Neurosci, 2022 A 4‐tuple (y, x, v, w) in a graph is a 3‐arc if each of (y, x, v) and (x, v, w) is a path. The 3‐arc graph of H is the graph with vertex set all arcs of H and edge set containing all edges joining xy and vw whenever (y, x, v, w) is a 3‐arc of H. A Hamilton cycle is a closed path meeting each vertex of a graph.
Xu G, Sun Q, Liang Z.
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Hamiltonian cycles in planar cubic graphs with facial 2-factors, and a new partial solution of Barnette's Conjecture. [PDF]
J Graph Theory, 2021 Abstract We study the existence of hamiltonian cycles in plane cubic graphs G having a facial 2‐factor Q. Thus hamiltonicity in G is transformed into the existence of a (quasi) spanning tree of faces in the contraction G ∕ Q. In particular, we study the case where G is the leapfrog extension (called vertex envelope of a plane cubic graph G 0.
Bagheri Gh B +3 more
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SOME PROPERTIES ON COPRIME GRAPH OF GENERALIZED QUATERNION GROUPS
Barekeng, 2023 A coprime graph is a representation of finite groups on graphs by defining the vertex graph as an element in a group and two vertices adjacent to each other's if and only if the order of the two elements is coprime.
Arif Munandar
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On minimum degree conditions for supereulerian graphs [PDF]
, 1999 A graph is called supereulerian if it has a spanning closed trail. Let $G$ be a 2-edge-connected graph of order $n$ such that each minimal edge cut $E \subseteq E (G)$ with $|E| \le 3$ satisfies the property that each component of $G-E$ has order at ...
Broersma, H.J., Xiong, L.
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Notes on upper bounds for the largest eigenvalue based on edge-decompositions of a signed graph
Kuwait Journal of Science, 2023 The adjacency matrix of a signed graph has +1 or -1 for adjacent vertices, depending on the sign of the connecting edge. According to this concept, an ordinary graph can be interpreted as a signed graph without negative edges.
Zoran Stanić
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Spanning eulerian subdigraphs in semicomplete digraphs
Journal of Graph Theory, Volume 102, Issue 3, Page 578-606, March 2023., 2023 Abstract A digraph is eulerian if it is connected and every vertex has its in‐degree equal to its out‐degree. Having a spanning eulerian subdigraph is thus a weakening of having a hamiltonian cycle. In this paper, we first characterize the pairs (D,a) $(D,a)$ of a semicomplete digraph D $D$ and an arc a $a$ such that D $D$ has a spanning eulerian ...
Jørgen Bang‐Jensen +2 more
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Mathematics, 2023 Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem.
Noorsufia Abd Shukor +4 more
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Hamilton Powers of Eulerian Digraphs [PDF]
Electronic Journal of Combinatorics, 2022 Powers of graphs are well-studied combinatorial objects; it is well-known that the cube of an undirected graph is Hamiltonian, and Fleischner's theorem states that the square of a two-connected undirected graph is also Hamiltonian, resolving a conjecture
Enrico Col'on, John C. Urschel
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