Riga -point
Right closing almost conjugacy for G-shifts of finite type
A G-shift of finite type (G-SFT) is a shift of finite type which commutes with the continuous action of a finite group G. For irreducible G-SFTs we classify right closing almost conjugacy, answering a question of Bill Parry.
Rigid undirected graphs with given number of vertices
Rigidity and the lower bound Theorem l.
Rigidity of graph products of groups.
Ring elements as sums of units
In an Artinian ring R every element of R can be expressed as the sum of two units if and only if R/J(R) does not contain a summand isomorphic to the field with two elements. This result is used to describe those finite rings R for which Γ(R) contains a Hamiltonian cycle where Γ(R) is the (simple) graph defined on the elements of R with an edge between vertices r and s if and only if r - s is invertible. It is also shown that for an Artinian ring R the number of connected components of the graph...
Roman bondage in graphs
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 . The Roman domination number, , of G is the minimum weight of a Roman dominating function on G. In this paper, we define the Roman bondage of a graph G with maximum degree at least two to be the minimum cardinality of all sets E’ ⊆ E(G) for which ....
Room designs and one-factorizations.
Rotary hypermaps of genus 2.
Rotation and jump distances between graphs
A graph H is obtained from a graph G by an edge rotation if G contains three distinct vertices u,v, and w such that uv ∈ E(G), uw ∉ E(G), and H = G-uv+uw. A graph H is obtained from a graph G by an edge jump if G contains four distinct vertices u,v,w, and x such that uv ∈ E(G), wx∉ E(G), and H = G-uv+wx. If a graph H is obtained from a graph G by a sequence of edge jumps, then G is said to be j-transformed into H. It is shown that for every two graphs G and H of the same order (at least 5) and same...
Roughness in -graphs
-graphs are a type of graphs associated to groups, which were proposed by A. Bretto and A. Faisant (2005). In this paper, we first give some theorems regarding -graphs. Then we introduce the notion of rough -graphs and investigate some important properties of these graphs.
Route systems and bipartite graphs
Route systems of a connected graph
The concept of a route system was introduced by the present author in [3].Route systems of a connected graph generalize the set of all shortest paths in . In this paper some properties of route systems are studied.
Route systems on graphs
The well known types of routes in graphs and directed graphs, such as walks, trails, paths, and induced paths, are characterized using axioms on vertex sequences. Thus non-graphic characterizations of the various types of routes are obtained.
Routing and timetabling by topological search.