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The Electronic Journal of Combinatorics, 2010 For a graph G, its rth power is constructed by placing an edge between two vertices if they are within distance r of each other. In this note we study the amount of edges added to a graph by taking its rth power.
Pokrovskiy, Alexey
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PepGraphormer: an ESM-GAT hybrid deep learning framework for antimicrobial peptide prediction [PDF]
Journal of CheminformaticsThe prediction of Antimicrobial Peptides (AMPs) is a critical research area in drug discovery. Traditional methods, which rely on sequence alignment or handcrafted features, often fail to capture complex sequence-function relationships.
Changhang Lin +6 more
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On incidence coloring of graph fractional powers [PDF]
Opuscula Mathematica, 2022 For any \(n\in \mathbb{N}\), the \(n\)-subdivision of a graph \(G\) is a simple graph \(G^\frac{1}{n}\) which is constructed by replacing each edge of \(G\) with a path of length \(n\). The \(m\)-th power of \(G\) is a graph, denoted by \(G^m\), with the
Mahsa Mozafari-Nia, Moharram N. Iradmusa
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Queue Layouts of Graph Products and Powers [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 A k-queue layout of a graph G consists of a linear order σ of V(G), and a partition of E(G) into k sets, each of which contains no two edges that are nested in σ.
David R. Wood
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On Powers of Some Graph Operations [PDF]
Mathematics Interdisciplinary Research, 2018 Let G*H be the product * of G and H. In this paper we determine the rth power of the graph G*H in terms of Gr, Hrand Gr*Hr, when * is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation
Mohamed Seoud, Hamdy Mohamed Hafez
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Graph Powers and Graph Homomorphisms [PDF]
The Electronic Journal of Combinatorics, 2010 In this paper, we investigate some basic properties of fractional powers. In this regard, we show that for any non-bipartite graph $G$ and positive rational numbers ${2r+1\over 2s+1} < {2p+1\over 2q+1}$, we have $G^{2r+1\over 2s+1} < G^{2p+1\over 2q+1}$. Next, we study the power thickness of $G$, that is, the supremum of rational numbers ${2r+
Hajiabolhassan, Hossein, Taherkhani, Ali
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SOME GRAPH PARAMETERS OF POWER SET GRAPHS
Advances and Applications in Discrete Mathematics, 2021 In this study, we examine some graph parameters such as the edge number, chromatic number, girth, domination number and clique number of power set graphs.
Cangül, İsmail Naci +3 more
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The Bounds for the First General Zagreb Index of a Graph
Universal Journal of Mathematics and Applications, 2021 The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$.
Rao Li
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Chain graph reduction into power chain graphs
Quantitative and Computational Methods in Behavioral Sciences, 2021 Reduction of graphs is a class of procedures used to decrease the dimensionality of a given graph in which the properties of the reduced graph are to be induced from the properties of the larger original graph. This paper introduces both a new method for reducing chain graphs to simpler directed acyclic graphs (DAGs), that we call power chain graphs ...
Víthor Rosa Franco +3 more
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Forbidden Subgraphs of Power Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are connected by an edge between if and only if either $u=v^i$ or $v=u^j$ for some $i$, $j$.
Manna, Pallabi +2 more
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