Results 11 to 20 of about 270,997 (279)
A Study on the Nourishing Number of Graphs and Graph Powers
Mathematics, 2015 Let \(\mathbb{N}_{0}\) be the set of all non-negative integers and \(\mathcal{P}(\mathbb{N}_{0})\) be its power set. Then, an integer additive set-indexer (IASI) of a given graph \(G\) is defined as an injective function \(f:V(G)\to \mathcal{P}(\mathbb{N}
Sudev Naduvath, Germina Augustine
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A Conjecture Regarding the Extremal Values of Graph Entropy Based on Degree Powers
Entropy, 2016 Many graph invariants have been used for the construction of entropy-based measures to characterize the structure of complex networks. The starting point has been always based on assigning a probability distribution to a network when using Shannon’s ...
Kinkar Chandra Das, Matthias Dehmer
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The Shannon capacity of a graph and the independence numbers of its powers
IEEE Transactions on Information Theory, 2006 The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the strong graph product.
Alon, Noga, Lubetzky, Eyal
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Discrete Mathematics, 2009 In this paper, some results concerning the colorings of graph powers are presented. The notion of helical graphs is introduced. We show that such graphs are hom-universal with respect to high odd-girth graphs whose $(2t+1)$st power is bounded by a Kneser graph. Also, we consider the problem of existence of homomorphism to odd cycles. We prove that such
Hossein Hajiabolhassan
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Power up! Robust Graph Convolutional Network via Graph Powering
Proceedings of the AAAI Conference on Artificial Intelligence, 2021 Graph convolutional networks (GCNs) are powerful tools for graph-structured data. However, they have been recently shown to be vulnerable to topological attacks. To enhance adversarial robustness, we go beyond spectral graph theory to robust graph theory.
Jin, Ming +3 more
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Quotient graphs for power graphs [PDF]
Rendiconti del Seminario Matematico della Università di Padova, 2017 In a previous paper of the first author a procedure was developed for counting the components of a graph through the knowledge of the components of one of its quotient graphs. Here we apply that procedure to the proper power graph \mathcal{P}_0(G ...
BUBBOLONI, DANIELA +2 more
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On \delta^(k)-colouring of Powers of Paths and Cycles
Theory and Applications of Graphs, 2021 In a proper vertex colouring of a graph, the vertices are coloured in such a way that no two adjacent vertices receive the same colour, whereas in an improper vertex colouring, adjacent vertices are permitted to receive same colours subjected to some ...
Merlin Ellumkalayil, Sudev Naduvath
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Note on the Sum of Powers of Normalized Signless Laplacian Eigenvalues of Graphs [PDF]
Mathematics Interdisciplinary Research, 2019 In this paper, for a connected graph G and a real α≠0, we define a new graph invariant σα(G)-as the sum of the alphath powers of the normalized signless Laplacian eigenvalues of G.
Ş. Burcu Bozkurt Altındağ
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An algorithmic analysis of Flood-It and Free-Flood-It on graph powers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Analysis of ...
Uéverton dos Santos Souza +2 more
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Clustering Powers of Sparse Graphs [PDF]
The Electronic Journal of Combinatorics, 2020 We prove that if $G$ is a sparse graph — it belongs to a fixed class of bounded expansion $\mathcal{C}$ — and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these clique to a single vertex again yields a sparse graph.
Nešetřil, Jaroslav +3 more
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