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The aim of this article is to introduce a new definition of domination number in graphs called hn-domination number denoted by . This paper presents some properties which show the concepts of connected and independent hn-domination.
Omran et al.
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On independent domination number of regular graphs
A subset \(S\) of the vertex set of a graph \(G\) is called independent, if no two of its vertices are adjacent in \(G\). An independent set in \(G\) is maximal, if it is not a proper subset of another independent set of \(G\). The minimum number of vertices of a maximal independent set is the independent domination number \(i(G)\) of \(G\).
Lam, Peter Che Bor +2 more
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An improvement on the maximum number of ‐dominating independent sets [PDF]
AbstractErdős and Moser raised the question of determining the maximum number of maximal cliques or, equivalently, the maximum number of maximal independent sets in a graph on vertices. Since then there has been a lot of research along these lines.A ‐dominating independent set is an independent set such that every vertex not contained in has at ...
Dániel Gerbner +4 more
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A synthetic benzoxazine dimer derivative targets c‐Myc to inhibit colorectal cancer progression
Benzoxazine dimer derivatives bind to the bHLH‐LZ region of c‐Myc, disrupting c‐Myc/MAX complexes, which are evaluated from SAR analysis. This increases ubiquitination and reduces cellular c‐Myc. Impairing DNA repair mechanisms is shown through proteomic analysis.
Nicharat Sriratanasak +8 more
wiley +1 more source
Aggressive prostate cancer is associated with pericyte dysfunction
Tumor‐produced TGF‐β drives pericyte dysfunction in prostate cancer. This dysfunction is characterized by downregulation of some canonical pericyte markers (i.e., DES, CSPG4, and ACTA2) while maintaining the expression of others (i.e., PDGFRB, NOTCH3, and RGS5).
Anabel Martinez‐Romero +11 more
wiley +1 more source
Outer-Independent Italian Domination in Graphs
An outer-independent Italian dominating function (OIIDF) on a graph G with vertex set V(G) is defined as a function f : V(G) → {0, 1, 2}, such that every vertex v ∈ V(G) with f(v) = 0 has at least two neighbors assigned 1 under f or one ...
Wenjie Fan +5 more
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ERRFI1, a neural crest (NC)‐associated gene, was upregulated in melanoma and negatively correlated with the expression of melanocytic differentiation markers and the susceptibility of melanoma cells toward BRAF inhibitors (BRAFi). Knocking down ERRFI1 significantly increased the sensitivity of melanoma cells to BRAFi.
Nina Wang +8 more
wiley +1 more source
Independent k-rainbow bondage number of graphs
For an integer [Formula: see text] an independent k-rainbow dominating function (IkRDF for short) on a graph G is a function g that assigns to each vertex a set of colors chosen from the subsets of [Formula: see text] satisfying the following conditions:
S. Kosari +4 more
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CDK11 inhibition stabilises the tumour suppressor p53 and triggers the production of an alternative p21WAF1 splice variant p21L, through the inactivation of the spliceosomal protein SF3B1. Unlike the canonical p21WAF1 protein, p21L is localised in the cytoplasm and has reduced cell cycle‐blocking activity.
Radovan Krejcir +12 more
wiley +1 more source
Computational Complexity of Outer-Independent Total and Total Roman Domination Numbers in Trees
An outer-independent total dominating set (OITDS) of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \ D is independent.
Zepeng Li +4 more
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