A Roman dominating function on a graph G = (V,E) is a function f : V −→ {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 is the value w(f) = ∑ v∈V f(v). The Roman domination number of a graph G, denoted by γR(G), equals the minimum weight of a Roman dominating function on ...

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

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

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value ω(f) = ∑ v∈V f(v). The k-distance Roman domination number ...

The establishment of a standing Roman army during the reign of Augustus resulted in an increased demand for military doctors. The knowledge about the Roman military medicine comes primarily from the excavations at the valetudinaria. Medical instruments, medicine containers and remains of medicinal plants found there indicate that the Roman army strived to provide unwell legionaries with excelle...

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(...

Librarian of the National Library ofWales, and used to illustrate the lecture at Cardiff. The initial article is a scholarly account of Thomas Baskerville, Elizabethan apothecary of Exeter, by Margery Rowe and G. E. Trease. To a Welsh reviewer, another pleasing feature of the Transactions is that it has been printed by J. D. Lewis and Sons Ltd., Gomerian Press, Llandysul. They have already done...