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What do Eulerian and Hamiltonian cycles have to do with genome assembly? [PDF]
PLoS Computational Biology, 2021 Many students are taught about genome assembly using the dichotomy between the complexity of finding Eulerian and Hamiltonian cycles (easy versus hard, respectively).
Paul Medvedev, Mihai Pop
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MathematicsIn this paper, we explore the connection between sensor networks and graph theory. Sensor networks represent distributed systems of interconnected devices that collect and transmit data, while graph theory provides a robust framework for modeling and ...
Manuel Ceballos, María Millán
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Eulerian subgraphs containing given vertices and hamiltonian line graphs
Discrete Mathematics, 1998 Let \(G\) be a graph and let \(D_1(G)\) be the set of vertices of degree 1 in \(G\). A graph is called an eulerian graph if it is connected and every vertex has even degree. An eulerian subgraph \(H\) of a graph \(G\) is called a dominating eulerian subgraph if \(G-V(H)\) is edgeless.
exaly +2 more sources
On some intriguing problems in Hamiltonian graph theory -- A survey [PDF]
, 1999 We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, $t$-tough graphs, and claw-free ...
Broersma, H.J.
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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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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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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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Electronic Journal of Graph Theory and Applications, 2013 This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.
Jemal Abawajy +2 more
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On pathos lict graph of a tree [PDF]
, 2003 In this paper, the concept of pathos lict graph of a tree is introduced. We present a characterization of those graphs whose pathos lict graphs are planar, outerplanar, maximal outerplanar, crossing number one, eulerian and ...
Chandrasekhar, R., Muddebihal, M.H.
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Catlin’s reduced graphs with small orders
AKCE International Journal of Graphs and Combinatorics, 2020 A graph is supereulerian if it has a spanning closed trail. Catlin in 1990 raised the problem of determining the reduced nonsupereulerian graphs with small orders, as such results are of particular importance in the study of Eulerian subgraphs and ...
Hong-Jian Lai +3 more
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