Results 61 to 70 of about 256,711 (164)
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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A Study on the Nourishing Number of Graphs and Graph Powers [PDF]
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 \(f:V(G)\to \mathcal{P}(\mathbb{N}_{0})\) such that the induced edge-function \(f^+:E(G) \to\mathcal{P}(\mathbb{N}_{0})\) defined by \
Naduvath, Sudev, Augustine, Germina
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Distinguishing Cartesian Powers of Graphs [PDF]
The Electronic Journal of Combinatorics, 2005 Given a graph $G$, a labeling $c:V(G) \rightarrow \{1, 2, \ldots, d\}$ is said to be $d$-distinguishing if the only element in ${\rm Aut}(G)$ that preserves the labels is the identity. The distinguishing number of $G$, denoted by $D(G)$, is the minimum $d$ such that $G$ has a $d$-distinguishing labeling.
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A Vertex Separator Problem for Power Graphs of Groups
MathematicsGiven a graph G, an st-connected vertex separator (CVS) problem refers to the search for a minimum connected component in G whose removal leaves the pair of nodes s and t in two disjoint components.
Haeder Younis Althoby +2 more
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Brooks’ theorem on powers of graphs
Discrete Mathematics, 2014 We prove that for $k\geq 3$, the bound given by Brooks' theorem on the chromatic number of $k$-th powers of graphs of maximum degree $Δ\geq 3$ can be lowered by 1, even in the case of online list coloring.
Bonamy, Marthe, Bousquet, Nicolas
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Simplicial complexes defined on groups
Open MathematicsThis study makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group, which are preserved by automorphisms of the group, and in many
Cameron Peter J.
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On groups with specified quotient power graphs [PDF]
International Journal of Group Theory, 2016 . In this paper we study some relations between the power andquotient power graph of a finite group. These interesting relations motivateus to find some graph theoretical properties of the quotient power graphand the proper quotient power graph of a ...
Mostafa Shaker, Mohammadali Iranmanesh
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Signless Laplacian spectrum of power graphs of finite cyclic groups
AKCE International Journal of Graphs and Combinatorics, 2020 In this paper, we have studied the Signless Laplacian spectrum of the power graph of finite cyclic groups. We have shown that is an eigen value of Signless Laplacian of the power graph of with multiplicity at least In particular, using the theory of ...
Subarsha Banerjee, Avishek Adhikari
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Zhongguo dianliAs the widespread integration of new energy and interconnection of large power grids, the operation modes of power systems are undergoing transformations, which leads to a fast surge in data volumes and higher demands for real-time information processing,
Pei ZHANG +8 more
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Automorphism group of certain power graphs of finite groups
Electronic Journal of Graph Theory and Applications, 2017 The power graph $\mathcal{P}(G)$ of a group $G$ is the graphwith group elements as vertex set and two elements areadjacent if one is a power of the other. The aim of this paper is to compute the automorphism group of the power graph of several well-known
Ali Reza Ashrafi +2 more
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