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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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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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On Eulerian and Hamiltonian Graphs and Line Graphs [PDF]
Canadian Mathematical Bulletin, 1965 A graph G has a finite set V of points and a set X of lines each of which joins two distinct points (called its end-points), and no two lines join the same pair of points. A graph with one point and no line is trivial. A line is incident with each of its end-points. Two points are adjacent if they are joined by a line.
C. St. J. A. Nash-Williams, Frank Harary
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EULERIAN AND HAMILTONIAN PROPERTIES OF GALLAI AND ANTI-GALLAI TOTAL GRAPHS [PDF]
Journal of the Indonesian Mathematical Society, 2015 Let $G = (V, E)$ be a graph. The \textit{Gallai total graph} $\Gamma_T(G)$ of $G$ is the graph, where $V(\Gamma_T(G))=V \cup E$ and $uv \in E(\Gamma_T(G))$ if and only if \begin{itemize} \item[$(i)$] $u$ and $v$ are adjacent vertices in $G$, or \item[$(ii)$] $u$ is incident to $v$ or $v$ is incident to $u$ in $G$, or \item[$(iii)$] $u$ and $v$ are ...
Shanu Goyal, Pravin Garg, Deepa Sinha
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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.
H. Lai
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Usage of Eulerian and Hamiltonian Graph in Pandemic Situation
Journal of Applied Science and Education (JASE), 2021 The existence of Euler and Hamiltonian graph make it easier to solve a real-life problem. During the time of pandemic “Covid-19”, it is very essential for each one of us to be vaccinated. Vaccination is done in the hospitals by using Eulerian and Hamiltonian graphs not only to prevent people from infecting but also to increase the speed of vaccination.
Ambrish Kr. Pandey, Shriya Kanchan
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Fuzzy Eulerian and Fuzzy Hamiltonian Graphs with Their Applications
International Journal of Recent Technology and Engineering (IJRTE), 2019 In this article we discussed prominence of Fuzzy Eulerian and Fuzzy Hamiltonian graphs. Fuzzy logic is introduced to study the uncertainty of the event. In Fuzzy set theory we assign a membership value to each element of the set which ranges from 0 to 1. The earnest efforts of the researchers are perceivable in the relevant establishment of the subject
Abdul. Muneera +2 more
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Hamiltonian problems in edge-colored complete graphs and eulerian cycles in edge-colored graphs : some complexity results [PDF]
RAIRO - Operations Research, 1996 Summary: In an edge-colored graph, we say that a path (cycle) is alternating if it has length at least 2 (3) and if any 2 adjacent edges of this path (cycle) have different colors. We give efficient algorithms for finding alternating factors with a minimum number of cycles and then, by using this result, we obtain polynomial algorithms for finding ...
Benkouar, A. +3 more
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On Eulerian subgraphs and hamiltonian line graphs
, 2023 On Eulerian subgraphs and hamiltonian line ...
Yikang Xie
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Two‐arc closed subsets of graphs [PDF]
Journal of Graph Theory, 2003 AbstractA subset of vertices of a graph is said to be 2‐arc closed if it contains every vertex that is adjacent to at least two vertices in the subset. In this paper, 2‐arc closed subsets generated by pairs of vertices at distance at most 2 are studied.
Chen, Zhi-Hong +4 more
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