Results 181 to 190 of about 42,191 (216)

Distribution of Vertex Degree in Web-Graphs

Combinatorics, Probability and Computing, 2006
We give results for the age-dependent distribution of vertex degree and number of vertices of given degree in the undirected web-graph process, a discrete random graph process introduced in [8]. For such processes we show that as $k \rightarrow \infty$, the expected proportion of vertices of degree $k$ has power law parameter $1+1/\eta$ where $\eta$ is
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Distance degrees of vertex-transitive graphs

Graphs and Combinatorics, 1989
In [4], a lower bound of distance degrees of distance degree regular graphs is obtained. In this paper, we prove that a lower bound will be improved in some cases of vertex-transitive graphs.
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Note on vertex degrees of planar graphs

Journal of Graph Theory, 1984
Let \(d_ 1,...,d_ 2\) 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.
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The vertex degrees of minimum spanning trees

European Journal of Operational Research, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Degree associated reconstruction number of certain connected graphs with unique end vertex and a vertex of degree n−2

Discrete Mathematics, Algorithms and Applications, 2016
A vertex-deleted subgraph of a graph [Formula: see text] is called a card of [Formula: see text] A card of [Formula: see text] with which the degree of the deleted vertex is also given is called a degree associated card (or dacard) of [Formula: see text] The degree associated reconstruction number (or drn) of a graph [Formula: see text] is the size of
A. Anu, S. Monikandan
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The vertex degree polynomial of some graph operations

2023
Summary: 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, Salestina, Ruby M., Alwardi, Anwar, Ahmed, Hanan   +3 more
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The maximum degree in a vertex-magic graph [PDF]

Australas. J Comb., 2004
Let \(G\) be a vertex-magic graph with \(v\) vertices, \(e\) edges and \(c\) components. In the paper it is proved that the maximum degree \(\Delta\) of \(G\) satisfies \(\Delta\leq \sqrt{(7e^2+(6c+5)e+c^2+3c)/v}-2\).
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Vertex degree sums for supereulerian bipartite digraphs

Applied Mathematics and Computation
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiaqi Li, Yi Zhang 0114
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Parameterized Graph Editing with Chosen Vertex Degrees

2008
We study the parameterized complexity of the following problem: is it possible to make a given graph r-regular by applying at most kelementary editing operations; the operations are vertex deletion, edge deletion, and edge addition. We also consider more general annotated variants of this problem, where vertices and edges are assigned an integer cost ...
Luke Mathieson, Stefan Szeider
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Vertex Degrees

2023
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