Add to ORKGPlacing degree constraints on the vertices of a path yields the definitions of uphill and downhill paths. Specifically, we say that a path π = v1, v2, ⋯ vk+1 is a downhill path if for every i, 1 ≤ i ≤ k, deg(v1) ≥ deg(vi+1). Conversely, a path π = u1, u2, ⋯ uk+1 is an uphill path if for every i, 1 ≤ i ≤ k, deg(u1) ≤ deg(ui+1). The downhill domination number of a graph G is defined to be the minimum cardinality of a set S of vertices such that every vertex in V lies on a downhill path from some vertex in S. The uphill domination number is defined as expected. We explore the properties of these invariants and their relationships with other invariants. We also determine a Vizing-like result for the downhill (respectively, uphill) domination nu...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
For a connected graph G = (V,E), a set D ⊆ V (G) is a dominating set of G if every vertex in V (G)−D...
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D h...
A path π = (v1, v2, . . . , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k,...
A path π = (v1, v2, ⋯ , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg...
Placing degree constraints on the vertices of a path allows the definitions of uphill and downhill p...
A path π = (v1, v2, . . . , vk+1) iun a graph G = (V, E) is a downhill path if for every i, 1 ≤ i ≤ ...
A path π = (v1, v2,...vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 \u3c i \u3c k,...
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is ad...
for inclusion in Undergraduate Honors Theses by an authorized administrator of Digital Commons @ Eas...
We study domination between different types of walks connecting two non-adjacent vertices u and v of...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(...
In a graph G = (V, E) each vertex is said to dominate every vertex in its closed neighborhood. In a ...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
For a connected graph G = (V,E), a set D ⊆ V (G) is a dominating set of G if every vertex in V (G)−D...
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D h...
A path π = (v1, v2, . . . , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k,...
A path π = (v1, v2, ⋯ , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg...
Placing degree constraints on the vertices of a path allows the definitions of uphill and downhill p...
A path π = (v1, v2, . . . , vk+1) iun a graph G = (V, E) is a downhill path if for every i, 1 ≤ i ≤ ...
A path π = (v1, v2,...vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 \u3c i \u3c k,...
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is ad...
for inclusion in Undergraduate Honors Theses by an authorized administrator of Digital Commons @ Eas...
We study domination between different types of walks connecting two non-adjacent vertices u and v of...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
Let G(V,E) be a finite, undirected, simple graph without isolated vertices. A dominating set D of V(...
In a graph G = (V, E) each vertex is said to dominate every vertex in its closed neighborhood. In a ...
For distinct vertices u and v of a nontrivial connected graph G, the detour distance D(u, v) between...
For a connected graph G = (V,E), a set D ⊆ V (G) is a dominating set of G if every vertex in V (G)−D...
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D h...