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Subdivision and graph eigenvalues
Linear Algebra and its ApplicationsThis paper investigates the asymptotic nature of graph spectra when some edges of a graph are subdivided sufficiently many times. In the special case where all edges of a graph are subdivided, we find the exact limits of the $k$-th largest and $k$-th smallest eigenvalues for any fixed $k$.
Hitesh Kumar +3 more
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Domination Subdivision and Domination Multisubdivision Numbers of Graphs
Discussiones Mathematicae Graph Theory, 2019 The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree
Dettlaff Magda +2 more
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IEEE Access, 2019 Let G be a connected graph. The subdivision graph S(G) of a graph (G) is the graph obtained by inserting a new vertex into every edge of G. The set of such new vertices is denoted by I(G).
Qun Liu
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On Topological Minors in Random Simplicial Complexes
, 2015 For random graphs, the containment problem considers the probability that a binomial random graph $G(n,p)$ contains a given graph as a substructure. When asking for the graph as a topological minor, i.e., for a copy of a subdivision of the given graph ...
Gundert, Anna, Wagner, Uli
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Journal of Combinatorial Theory, Series B, 1998 Given four distinct vertices in a 4-connected planar graph \(G\), we characterize when the graph \(G\) contains a \(K_4\)-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has no \(K_4\)-subdivision with specified degree three vertices, if ...
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Rainbow game domination subdivision number of a graph [PDF]
Romanian Journal of Mathematics and Computer Science, 2014 The rainbow game domination subdivision number of a graph G is defined by the following game. Two players D and A, D playing first, alternately mark or subdivide an edge of G which is not yet marked nor subdivided.
J. Amjadi
doaj
Prime labeling in the context of web graphs without center
AKCE International Journal of Graphs and Combinatorics, 2021 A prime labeling on a graph G of order n is a bijection from the set of vertices of G into the set of first n positive integers such that any two adjacent vertices in G have relatively prime labels.
A. N. Kansagara, S. K. Patel
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The Clique Problem in Ray Intersection Graphs
, 2011 Ray intersection graphs are intersection graphs of rays, or halflines, in the plane. We show that any planar graph has an even subdivision whose complement is a ray intersection graph.
Cabello, Sergio +2 more
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Reformulated Zagreb Indices of Some Derived Graphs
Mathematics, 2019 A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties.
Jia-Bao Liu +4 more
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Folding List of Graphs Obtained from a Given Graph
International Journal of Mathematics and Mathematical Sciences, 2020 In this paper, we examine the relation between graph folding of a given graph and foldings of new graphs obtained from this graph by some techniques like dual, gear, subdivision, web, crown, simplex, crossed prism, and clique-sum graphs. In each case, we
E. M. El-Kholy, H. Ahmed
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