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This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.
Jemal Abawajy +2 more
openaire +3 more sources
Graph classes with and without powers of bounded clique-width [PDF]
We initiate the study of graph classes of power-bounded clique-width, that is, graph classes for which there exist integers $k$ and $\ell$ such that the $k$-th powers of the graphs are of clique-width at most $\ell$.
Safe, Martín D. +6 more
core +2 more sources
On the multipacking number of grid graphs [PDF]
In 2001, Erwin introduced broadcast domination in graphs. It is a variant of classical domination where selected vertices may have different domination powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted $\gamma_b(G)$.
Laurent Beaudou, Richard C. Brewster
doaj +1 more source
Summary: We define a new graph operation called the \(k\)th inner power. The construction-which is somewhat analogous to the \(k\)th power with respect to the direct product-seems to lend itself nicely to certain questions concerning cancellation over the direct product.
Richard H. Hammack, Neal Livesay
openaire +3 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Min Zhao, Liying Kang, Gerard J. Chang
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In this study, we found that human cervical‐derived adipocytes maintain intracellular iron level by regulating the expression of iron transport‐related proteins during adrenergic stimulation. Melanotransferrin is predicted to interact with transferrin receptor 1 based on in silico analysis.
Rahaf Alrifai +9 more
wiley +1 more source
Power domination in Kn\"odel graphs and Hanoi graphs
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Varghese, Seethu +2 more
openaire +3 more sources
Average Degree in Graph Powers [PDF]
AbstractThe kth power of a simple graph G, denoted by , is the graph with vertex set where two vertices are adjacent if they are within distance k in G. We are interested in finding lower bounds on the average degree of . Here we prove that if G is connected with minimum degree and , then G4 has average degree at least .
Matt DeVos +2 more
openaire +3 more sources
Biophysical approaches for studying viral entry
Viruses infect all living organisms and have been responsible for major epidemics and pandemics. Their ongoing evolutionary battle with host defenses creates a constant need for improved tools to study viral behavior. Advancing methods to probe viral attachment, fusion, and genome release deepen our understanding of how infections begin and support the
Inbar Yosibash, Raya Sorkin
wiley +1 more source
Cyclic labellings with constraints at two distances [PDF]
Motivated by problems in radio channel assignment, we consider the vertex-labelling of graphs with non-negative integers. The objective is to minimise the span of the labelling, subject to constraints imposed at graph distances one and two.
S D Noble +3 more
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