Results 301 to 310 of about 3,967,804 (356)
Fringe Trees for Random Trees With Given Vertex Degrees
Random Structures & Algorithms, 2023 We prove asymptotic normality for the number of fringe subtrees isomorphic to any given tree in uniformly random trees with given vertex degrees. As applications, we also prove corresponding results for random labeled trees with given vertex degrees, for
Gabriel Berzunza Ojeda +2 more
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Vertex Arboricity and Vertex Degrees
Graphs and Combinatorics, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
D. Bauer, A. Nevo, E. Schmeichel
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Vertex Degrees in Planar Graphs
Planar Graphs, 1991D. West, Tood Will
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On Making a Distinguished Vertex of Minimum Degree by Vertex Deletion
Algorithmica, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Betzler, Nadja +4 more
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International Journal of Quantum Chemistry
A novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices.
Ivan Gutman, Boris Furtula, M. Oz
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A novel geometric method is proposed for constructing vertex‐degree‐based molecular structure descriptors (topological indices). The model is based on an ellipse whose focal points represent the degrees of a pair of adjacent vertices.
Ivan Gutman, Boris Furtula, M. Oz
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Note on vertex degrees of planar graphs
Journal of Graph Theory, 1984Let \(d_ 1,...,d_ 2\) denote the degree sequence of a graph, and let \(M_ 2=\sum^{n}_{i=1}d^ 2_ i.\) The author shows that if G is an outerplanar graph of order \(n\geq 3\) then \(M_ 2\leq n^ 2+7n-18.\) Also if G is a planar graph of order \(n\geq 4\) then \(M_ 2\leq 2n^ 2+12n-44.\) These results are proved by induction on n.
Miroslaw Truszczyáski
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Degree sum and vertex dominating paths
Journal of Graph Theory, 2018AbstractA vertex dominating path in a graph is a path P such that every vertex outside P has a neighbor on P. In 1988 H. Broersma [5] stated a result implying that every n‐vertex k‐connected graph G such that contains a vertex dominating path. We provide a short, self‐contained proof of this result and further show that every n‐vertex k‐connected ...
Jill Faudree +4 more
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Trees with Maximum Vertex-Degree-Based Topological Indices
Match Communications in Mathematical and in Computer Chemistry, 2022Summary: Let \(G\) be a graph with vertex set \(V(G)=\{v_1,v_2,\dots,v_n\}\) and edge set \(E(G)\), and \(d(v_i)\) be the degree of the vertex \(v_i\). The definition of a vertex-degree-based topological index of \(G\) is as follows \[ \mathcal{T}_f=\mathcal{T}_f(G)=\sum\limits_{v_iv_j\in E(G)}f(d(v_i),d(v_j)), \] where \(f(x,y)>0\) is a symmetric real
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The vertex degree polynomial of some graph operations
2023Summary: Graph polynomials have been developed for measuring structural information of networks using combinatorial graph invariants and for characterizing graphs. Various problems in graph theory and discrete mathematics can be treated and solved in a rather efficient manner by making use of polynomials.
CANGÜL, İSMAİL NACİ +3 more
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On Making a Distinguished Vertex Minimum Degree by Vertex Deletion
2011For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in) degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis.
Nadja Betzler +3 more
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