‎A Roman dominating function (RDF) on a graph G=(V,E) is a function  f : V → {0, 1, 2}  such that every vertex u for which f(u)=0 is‎ ‎adjacent to at least one vertex v for which f(v)=2‎. ‎An RDF f is called‎‎an outer independent Roman dominating function (OIRDF) if the set of‎‎vertices assigned a 0 under f is an independent set‎. ‎The weight of an‎‎OIRDF is the sum of its function values over ...

Rainbow connection number rc(G) of a connected graph G is the minimum number of colours needed to colour the edges of G, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we show that for every connected graph G, with minimum degree at least 2, the rainbow connection number is upper bounded by γc(G) + 2, where γc(G) is th...

Let k ∈ N and let G be a graph. A function f : V (G) → 2 is a rainbow function if, for every vertex x with f(x) = ∅, f(N(x)) = [k]. The rainbow domination number γkr(G) is the minimum of ∑ x∈V (G) |f(x)| over all rainbow functions. We investigate the rainbow domination problem for some classes of perfect graphs.

We study correlation functions in the complex fermion SYK model. focus, specifically, on h=2 mode which explicitly breaks conformal invariance and exhibits chaotic behaviour. numerically explore a six-point OTOC, with two three real-time folds, respectively. While our approach is expected to yield an early-time growth, we nevertheless observe near-maximal value. Following program of Gross-Rosen...

We give an 0 (nlogln) [ime algorirnm for finding a minimum independem dominating se[ in a pennmation graph. TItis improves on ilie previous D(n 3) time algorictun known for solving tllis problem [4]. .,. Dept of CompUlcr Sci., Purdue Univ., West Gf:tyelle, IN 47907. Rcso::trch ~upported by ONR. Contr:lct NOOOI-l-34-K. 0502:md NSF Gl':tnl DCR-8451393, wilh matching funds from AT&T. • o.:pt of Ma...