Let D be a finite and simple digraph with vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and x∈N−[v] f(x) ≥ k for each v ∈ V (D), where N−[v] consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A set {f1, f2, . . . , fd} of distinct signed k-dominating functions on D with the property that ...

A signed Roman dominating function on the digraphD is a function f : V (D) −→ {−1, 1, 2} such that ∑ u∈N−[v] f(u) ≥ 1 for every v ∈ V (D), where N−[v] consists of v and all inner neighbors of v, and every vertex u ∈ V (D) for which f(u) = −1 has an inner neighbor v for which f(v) = 2. A set {f1, f2, . . . , fd} of distinct signed Roman dominating functions on D with the property that ∑d i=1 fi(...

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Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....

A graph G is equitably k-choosable if for every k-list assignment L there exists an L-coloring of G such that every color class has at most d|G|/ke vertices. We prove results towards the conjecture that every graph with maximum degree at most r is equitably (r+1)choosable. In particular, we con rm the conjecture for r ≤ 7 and show that every graph with maximum degree at most r and at least r ve...

For a given $2$-partition $(V_1,V_2)$ of the vertices of a (di)graph $G$, we study properties of the spanning bipartite subdigraph $B_G(V_1,V_2)$ of $G$ induced by those arcs/edges that have one end in each $V_i$. We determine, for all pairs of non-negative integers $k_1,k_2$, the complexity of deciding whether $G$ has a 2-partition $(V_1,V_2)$ such that each vertex in $V_i$ has at least $k_i$ ...

In this paper, we explore a new problem of mining general temporal association rules in publication databases. In essence, a publication database is a set of transactions where each transaction T is a set of items of which each item contains an individual exhibition period. The current model of association rule mining is not able to handle the publication database due to the following fundament...

Abstract Research collaborations between global north and south have a long history in studies of forced migration, discussions power relations such research relationships existed for time. We are two researchers working across the south–north divide, this article reflects on our attempt to navigate industry amid ‘Syrian refugee complex’. discuss carve out space more equitable north–south divid...