For a graph $G=(V(G),E(G))$, an Italian dominating function (ID function) $f:V(G)\rightarrow\{0,1,2\}$ has the property that for every vertex $v\in V(G)$ with $f(v)=0$, either $v$ is adjacent to assigned $2$ under $f$ or least two vertices $1$ $f$. The weight of ID $\sum_{v\in V(G)}f(v)$. domination number minimum taken over all functions $G$. In this paper, we initiate study variant functions....

Preloaded and nonpreloaded dieters (restrained eaters) and nondieters (unrestrained eaters) completed a modified version of the Stroop task to measure selective biases in cognitive processing. In two separate studies, a milkshake preload led to increased cognitive interference for body shape words, especially for restrained eaters. There were no differences between restrained and unrestrained e...

Implicit self-esteem and its link to body shape and weight concerns were examined among restrained (n=32) and unrestrained eaters (n=39). Implicit self-esteem was assessed in an Implicit Association Test before and after increasing the participants' awareness of their own body shape and weight. The results showed a differential direction of change of implicit self-esteem in both groups: Whereas...

Let G = (V,E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. We show that if T is a tree of order n, then γtr(T ) ≥ d(n + 2)/2e. Moreover, we s...

Most involuntary memories are elicited by external cues (e.g., smells, sounds) that have unique associations with specific memories (Berntsen's cue-retrieval hypothesis), but involuntary memories can sometimes be elicited by weak, even imperceptible, cues that raise the activation level of an already primed memory (Berntsen's motivation-priming hypothesis) to also reach conscious awareness duri...

OBJECTIVE Two studies examined the influence of meal-size information on restrained and unrestrained eaters' judgments of body weight and size. METHOD In Study 1, restrained and unrestrained eaters made body-weight and body-size judgments of a woman who had eaten either a small meal or a large meal. In Study 2, participants watched a video of a woman eating a small or large meal, and selected...