Results 21 to 30 of about 3,157 (213)
Permutational Powers of a Graph [PDF]
The Electronic Journal of Combinatorics, 2019 This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the classical zig-zag product of graphs when the permutation is an involution, and it is in fact more ...
Matteo Cavaleri +2 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 $i$, $j$.
Pallabi Manna +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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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 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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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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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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Theoretical Computer Science, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andreas Brandstädt, Van Bang Le
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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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