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Domination subdivision numbers in graphs
2004A set \(S\) of vertices of a graph \(G\) is a dominating set if each vertex outside \(S\) has a neighbor in \(S\). The domination number \(\gamma(G)\) of \(G\) is the minimum cardinality of a dominating set of \(G\). An edge \(uv\) in \(G\) is subdivided if the edge \(uv\) is deleted, but a new vertex \(x\) is added, along with two new edges \(xu\) and
Favaron, Odile +2 more
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COHERENCE ANALYSIS FOR ITERATED LINE GRAPHS OF MULTI-SUBDIVISION GRAPH
Fractals, 2020More and more attention has focused on consensus problem in the study of complex networks. Many researchers investigated consensus dynamics in a linear dynamical system with additive stochastic disturbances. In this paper, we construct iterated line graphs of multi-subdivision graph by applying multi-subdivided-line graph operation. It has been proven
MEIFENG DAI +5 more
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Combinatorics, Probability and Computing, 1996
In 1964 Dirac conjectured that every graph with n vertices and at least 3n − 5 edges contains a subdivision of K5 We prove a weakened version with 7/2;n − 7 instead of 3n − 5. We prove that, for any prescribed vertex νo, the subdivision can be found such that νo is not one of the five branch vertices.
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In 1964 Dirac conjectured that every graph with n vertices and at least 3n − 5 edges contains a subdivision of K5 We prove a weakened version with 7/2;n − 7 instead of 3n − 5. We prove that, for any prescribed vertex νo, the subdivision can be found such that νo is not one of the five branch vertices.
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Degree Condition for Subdivisions of Unicyclic Graphs
Graphs and Combinatorics, 2008The authors prove the following results: Let \(H\) be any graph of order \(n\) with \(k\) vertex disjoint pieces \(H_1,\dots, H_k\), each of which contains at most one cycle. Let \(G\) be any graph of order at least \(n\) with \(\delta (G) \geq n -k \). Then \(G\) contains a cyclic subdivision of \(H\).
BABU, C, DIWAN, A
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Antimagic labeling for subdivisions of graphs
Discrete Applied MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Spatial Subdivision of Gabriel Graph
2015Gabriel graph is one of the well-studied proximity graphs which has a wide range of applications in various research areas such as wireless sensor network, gene flow analysis, geographical variation analysis, facility location, cluster analysis, and so on. In numerous applications, an important query is to find a specific location in a Gabriel graph at
M. Z. Hossain +3 more
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Subdivisions and the chromatic index of r‐graphs
Journal of Graph Theory, 1996Let \(T_2\) be the graph obtained from the Petersen graph by first deleting a vertex and then contracting an edge incident to a vertex of degree two. We give a simple characterization of the graphs that contain no subdivision of \(T_2\). This characterization is used to show that if every planar \(r\)-graph is \(r\)-edge colorable, then every \(r ...
Kilakos, K., Shepherd, F. B.
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Acyclic Colorings of Graph Subdivisions
2011An acyclic coloring of a graph G is a coloring of the vertices of G, where no two adjacent vertices of G receive the same color and no cycle of G is bichromatic. An acyclic k-coloring of G is an acyclic coloring of G using at most k colors. In this paper we prove that any triangulated plane graph G with n vertices has a subdivision that is acyclically ...
Debajyoti Mondal +3 more
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
Subdivision Graph, Power and Line Graph of a Soft Graph
Communications in Mathematics and Applications, 2022Rajesh K. Thumbakara +2 more
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