Skolem-type difference sets for cycle systems.
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...
On strong digraphs with a prescribed ultracenter
The (directed) distance from a vertex to a vertex in a strong digraph is the length of a shortest - (directed) path in . The eccentricity of a vertex of is the distance from to a vertex furthest from in . The radius rad is the minimum eccentricity among the vertices of and the diameter diam is the maximum eccentricity. A central vertex is a vertex with eccentricity and the subdigraph induced by the central vertices is the center . For a central vertex in a strong digraph...
On signed degrees in signed graphs
Stratidistance in stratified graphs
A graph is a stratified graph if its vertex set is partitioned into classes (each of which is a stratum or a color class). A stratified graph with strata is -stratified. If is a connected -stratified graph with strata where the vertices of are colored , then the -proximity of a vertex of is the distance between and a vertex of closest to . The strati-eccentricity of is . The minimum strati-eccentricity over all vertices of is the...
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