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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 its quotient graphs. We apply here that procedure to the proper power graph $\mathcal{P}_0(G)$ of a finite
Bubboloni, D. +2 more
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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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Power domination in maximal planar graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 Power domination in graphs emerged from the problem of monitoring an electrical system by placing as few measurement devices in the system as possible. It corresponds to a variant of domination that includes the possibility of propagation.
Paul Dorbec +2 more
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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Descending endomorphism graphs of groups
AKCE International Journal of Graphs and Combinatorics, 2023 We define a new type of graph of a group with reference to the descending endomorphisms of the group. A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. We define the
Vinay Madhusudanan +2 more
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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph.
Evi Yuniartika Asmarani +5 more
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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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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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