Results 11 to 20 of about 254,638 (264)
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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THE POWER GRAPH REPRESENTATION FOR INTEGER MODULO GROUP WITH POWER PRIME ORDER
Barekeng, 2023 There are many applications of graphs in various fields. Starting from chemical problems, such as the molecular shape of a compound to internet network problems, we can also use graphs to depict the abstract concept of a mathematical structure..
Lalu Riski Wirendra Putra +4 more
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The Wiener, hyper-Wiener, Harary and SK indices of the P(Z_{p^k.q^r}) power graph [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 The undirected P(Zₙ) power graph of a finite group of Zₙ is a connected graph, the set of vertices of which is Zₙ. Here u,v∈P(Zₙ) are two diverse adjacent vertices if and only if u≠v and ⟨v⟩ ⊆ ⟨u⟩ or ⟨u⟩ ⊆ ⟨v⟩.
Volkan Aşkin
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On the Regular Power Graph on the Conjugacy Classes of Finite Groups [PDF]
Mathematics Interdisciplinary Research, 2018 The (undirected) power graph on the conjugacy classes PC(G) of a group G is a simple graph in which the vertices are the conjugacy classes of G and two distinct vertices C and C' are adjacent in PC(G) if one is a subset of a power of the other.
Sajjad Mahmood Robati
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The rainbow connection number of the enhanced power graph of a finite group
Electronic Journal of Graph Theory and Applications, 2023 Let G be a finite group. The enhanced power graph ΓGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow connection number of ΓGe.
Luis A. Dupont +2 more
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Recent developments on the power graph of finite groups – a survey
AKCE International Journal of Graphs and Combinatorics, 2021 Algebraic graph theory is the study of the interplay between algebraic structures (both abstract as well as linear structures) and graph theory. Many concepts of abstract algebra have facilitated through the construction of graphs which are used as tools
Ajay Kumar +3 more
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The b-chromatic number of power graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 The b-chromatic number of a graph G is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i, with 1 ≤ i≤ k, has at least one representant x_i adjacent to a vertex of
Brice Effantin, Hamamache Kheddouci
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Construction Technology of Knowledge Graph and its Application in Power Grid [PDF]
E3S Web of Conferences, 2021 With the rapid development of energy internet, dispatchers need to learn more knowledge with wider scope and fast update speed. It’s urgent to realize the knowledge electrification, knowledge systematization, knowledge visualization and knowledge sharing
Xiaoping Gai +5 more
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Theoretical Computer Science, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas Brandstädt, Van Bang Le
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On the Structure of the Power Graph and the Enhanced Power Graph of a Group
The Electronic Journal of Combinatorics, 2017 Let $G$ be a group. The power graph of $G$ is a graph with the vertex set $G$, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique ...
Ghodratollah Aalipour +4 more
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