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Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey [PDF]
, 2021 Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also ...
Gabrys, Bogdan +2 more
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Splitting an Expander Graph [PDF]
Journal of Algorithms, 1999 The authors consider partitions \(E = E_1 \cup E_2 \cup\cdots\cup E_k\) of the edge set of an \(r\)-regular expander graph \(G = (V,E)\) such that the graphs \(G_i = (V,E_i)\) are expanders. Certain algorithms for finding edge disjoint paths use such partitions. A nonconstructive proof using the Lovász local lemma shows that very good partitions exist.
Molloy, M., Frieze, A.
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Minimal toughness in special graph classes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Let $t$ be a positive real number. A graph is called $t$-tough if the removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$ components, and all graphs are considered 0-tough. The toughness of a graph is the largest $t$ for which
Gyula Y. Katona, Kitti Varga
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Splitting Plane Graphs to Outerplanarity
Journal of Graph Algorithms and Applications, 2023 Vertex splitting replaces a vertex by two copies and partitions its incident edges amongst the copies. This problem has been studied as a graph editing operation to achieve desired properties with as few splits as possible, most often planarity, for which the problem is NP-hard.Here we study how to minimize the number of splits to turn a plane graph ...
Gronemann, Martin +2 more
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Ideal based graph structures for commutative rings
Cubo, 2022 We introduce a graph structure $\gamrr$ for commutative rings with unity. We study some of the properties of the graph $\gamrr$. Also we study some parameters of $\gamrr$ and find rings for which $\gamrr$ is split.
M. I. Jinnah, Shine C. Mathew
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Some structural graph properties of the non-commuting graph of a class of finite Moufang loops
Electronic Journal of Graph Theory and Applications, 2020 For any non-abelian group G, the non-commuting graph of G, Γ=ΓG, is a graph with vertex set G \ Z(G), where Z(G) is the set of elements of G that commute with every element of G and distinct non-central elements x and y of G are joined by an edge if and ...
Hamideh Hasanzadeh Bashir +1 more
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k-Zumkeller Graphs through Splitting of Graphs
Proyecciones (Antofagasta), 2023 Let G = (V,E) be a simple graph with vertex set V and edges set E. A 1−1 function f : V → N is said to induce a k-Zumkeller graph G if the induced edge function f ∗ : E → N defined by f ∗(xy) = f(x)f(y) satisfies the following conditions: f ∗(xy) is a Zumkeller number for every xy ∈ E. The total distinct Zumkeller numbers on the edges of G is k.
M. Kalaimathi, B. J. Balamurugan
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The local metric dimension of split and unicyclic graphs
Indonesian Journal of Combinatorics, 2022 A set W is called a local resolving set of G if the distance of u and v to some elements of W are distinct for every two adjacent vertices u and v in G. The local metric dimension of G is the minimum cardinality of a local resolving set of G.
Dinny Fitriani +3 more
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Degree associated edge reconstruction number of split graphs with biregular independent set is one
AKCE International Journal of Graphs and Combinatorics, 2020 A degree associated edge card of a graph G is an edge deleted subgraph of G with which the degree of the deleted edge is given. The degree associated edge reconstruction number of a graph G (or dern(G)) is the size of the smallest collection of the ...
N. Kalai Mathi, S. Monikandan
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Minimum Neighborhood Domination of Split Graph of Graphs
مجلة بغداد للعلوم, 2023 Let be a non-trivial simple graph. A dominating set in a graph is a set of vertices such that every vertex not in the set is adjacent to at least one vertex in the set.
ANJALINE. W, A.STANIS ARUL MARY
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