CHARACTERIZATION OF GRAPHS WITH EQUAL DOMINATION AND INDEPENDENT DOMINATION NUMBERS
Let $G$ be a finite simple graph. The domination number $\gamma(G)$ is the minimum cardinality of a dominating set, whereas the independent domination number $i(G)$ is the minimum cardinality of a dominating set that is also independent. Since every independent dominating set is a dominating set, $\gamma(G) \leq i(G)$ for every graph $G$.
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To mimic the elevated intestinal fluid pressure in breast cancers, we loaded human breast cancer cells (MCF‐7, MDA‐MB‐453, and BT‐474) to 50 mmHg hydrostatic pressure. Hydrostatic pressure exposure upregulated HIF‐1α and induced stemness in MCF‐7 and BT‐474 cells.
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Lower bounds for the Zagreb indices of trees with given total domination number and its applications in QSPR studies of alkanes. [PDF]
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On the Independent Domination Number of Random Regular Graphs
A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either in v ∈ D or there exists a vertex u ∈ D that is adjacent to v. We are interested in finding dominating sets of small cardinality.
W. Duckworth, N. C. Wormald
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