Let $kgeq 1$ be an integer, and let $G$ be a graph. A {it$k$-rainbow dominating function} (or a {it $k$-RDF}) of $G$ is afunction $f$ from the vertex set $V(G)$ to the family of all subsetsof ${1,2,ldots ,k}$ such that for every $vin V(G)$ with$f(v)=emptyset $, the condition $bigcup_{uinN_{G}(v)}f(u)={1,2,ldots,k}$ is fulfilled, where $N_{G}(v)$ isthe open neighborhood of $v$. The {it weight} o...

Dr Giorgio Zavagno ([email protected]) Dr Gianluca De Salvo ([email protected]) Dario Casara ([email protected]) Paola Del Bianco ([email protected]) Domenico Rubello ([email protected]) Fabrizio Meggiolaro ([email protected]) Carlo Riccardo Rossi ([email protected]) Mariaelena Pierobon ([email protected]) Mario Lise (mario.lise@unip...

For a graph G=(V,E) with V=V(G) and E=E(G), perfect double Italian dominating function is f:V→{0,1,2,3} having the property that 3≤∑u∈NG[v]f(u)≤4, for every vertex v∈G f(v)∈{0,1}. The weight of f sum f(V)=∑v∈V(G)f(v) minimum on G domination number γdIp(G) G. We initiate study functions. check γdIp some standard graphs evaluate γdI such graphs. functions versus Roman are perused. NP-completeness...

A concert pianist recorded her practice as she learned the third movement, Presto, of J.S. Bach's Italian Concerto. She also described the formal structure of the piece and reported her decisions about basic features (e.g., fingering), interpretive features (e.g., phrasing), and cues to attend to during performance (performance cues). These descriptions were used to identify which locations, fe...

Studies in human and non-human primates indicate that basic socio-cognitive operations are inherently linked to the power of gaze in capturing reflexively the attention of an observer. Although monkey studies indicate that the automatic tendency to follow the gaze of a conspecific is modulated by the leader-follower social status, evidence for such effects in humans is meager. Here, we used a g...

A subset X of edges of a graph G is called an edge dominating set of G if every edge not in X is adjacent to some edge in X . The edge domination number γ′(G) of G is the minimum cardinality taken over all edge dominating sets of G. An edge Roman dominating function of a graph G is a function f : E(G) → {0, 1, 2} such that every edge e with f(e) = 0 is adjacent to some edge e′ with f(e′) = 2. T...

We study, for a countably categorical theory T, the complexity of computing and the complexity of dominating the function specifying the number of n-types consistent with T.

A Roman dominating function (RDF) on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex v for which f(v) = 0, is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function f is the value f(V (G)) = ∑ v∈V (G) f(v). The Roman domination number of G, denoted by γR(G), is the minimum weight of an RDF on G. For a given graph,...

Acknowledgements I would like to express my deepest appreciation to my supervisors Professor Hans-Jürgen Schmeisser and Professor Winfried Sickel for their support and many hints and comments. I thank also Professor Hans Triebel for many valuable discussions on the topic of this work.