Domination and Independent Domination in Extended Supergrid Graphs
Supergrid graphs are derived by computing stitch paths for computerized embroidery machines. In the past, we have studied the Hamiltonian-related properties of supergrid graphs and their subclasses of graphs. In this paper, we propose a generalized graph
Jong-Shin Chen +3 more
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Inequalities involving independence domination, f-domination, connected and total f-domination numbers [PDF]
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Disordered but rhythmic—the role of intrinsic protein disorder in eukaryotic circadian timing
Unstructured domains known as intrinsically disordered regions (IDRs) are present in nearly every part of the eukaryotic core circadian oscillator. IDRs enable many diverse inter‐ and intramolecular interactions that support clock function. IDR conformations are highly tunable by post‐translational modifications and environmental conditions, which ...
Emery T. Usher, Jacqueline F. Pelham
wiley +1 more source
A note on domination and independence-domination numbers of graphs
Vizing's conjecture is true for graphs G satisfying γ i ( G ) = γ ( G ), where γ ( G ) is the domination number of a graph G and γ i ( G ) is the independence-domination number of G , that is, the maximum, over all independent sets I in G , of the minimum number of vertices needed to dominate I . The equality γ i ( G ) = γ (
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Domination and independence number of large 2-crossing-critical graphs
18 pages, 15 ...
Iršič, Vesna +4 more
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Protein pyrophosphorylation by inositol pyrophosphates — detection, function, and regulation
Protein pyrophosphorylation is an unusual signaling mechanism that was discovered two decades ago. It can be driven by inositol pyrophosphate messengers and influences various cellular processes. Herein, we summarize the research progress and challenges of this field, covering pathways found to be regulated by this posttranslational modification as ...
Sarah Lampe +3 more
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Bounds on Co-Independent Liar’s Domination in Graphs
A set S⊆V of a graph G=V,E is called a co-independent liar’s dominating set of G if (i) for all v∈V, NGv∩S≥2, (ii) for every pair u,v∈V of distinct vertices, NGu∪NGv∩S≥3, and (iii) the induced subgraph of G on V−S has no edge.
K. Suriya Prabha +3 more
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Time after time – circadian clocks through the lens of oscillator theory
Oscillator theory bridges physics and circadian biology. Damped oscillators require external drivers, while limit cycles emerge from delayed feedback and nonlinearities. Coupling enables tissue‐level coherence, and entrainment aligns internal clocks with environmental cues.
Marta del Olmo +2 more
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Graph polynomials for a class of DI-pathological graphs
Let be a simple graph. A dominating set is a set such that the closed neighborhood of is the entire vertex set. An independence set of a graph is a subset of vertices that are pairwise non-adjacent.
James M. Hammer, Joshua Harrington
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A characterization of trees with equal 2-domination and 2-independence numbers [PDF]
A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$.
Christoph Brause +2 more
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