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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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COMPUTATION OF VERTEX DEGREE ENERGY OF A GRAPH
Advances and Applications in Discrete Mathematics, 2017Summary: Using Huckel molecular orbital (HMO) theory of total \(\pi\)-electron energy, \textit{I. Gutman} [Ber. Math.-Stat. Sekt. Forschungszent. Graz 103, 22 S. (1978; Zbl 0402.05040)] conceived the idea of energy of a graph with the help of adjacency matrix. Adjacent atoms may or may not have same degree.
Kanna, M. R. Rajesh +2 more
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Distribution of Vertex Degree in Web-Graphs
Combinatorics, Probability and Computing, 2006We 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, 1989In [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, 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.
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The vertex degrees of minimum spanning trees
European Journal of Operational Research, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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
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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Vertex degree sums for supereulerian bipartite digraphs
Applied Mathematics and ComputationzbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jiaqi Li, Yi Zhang 0114
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