Abstract Seymour's Second Neighborhood Conjecture (SSNC) asserts that every finite
oriented graph has a vertex whose second out-neighborhood is at least as large as its first …

Abstract Seymour's Second Neighborhood Conjecture (SNC) asserts that every oriented
graph has a vertex whose second out-neighborhood is at least as large as its first out …

Abstract Seymour's Second Neighborhood Conjecture states that every simple oriented
graph has a vertex such that the cardinality of its second neighborhood is greater than or …

A digraph $ D=(V, E) $ is $ k $-transitive if for any directed $ uv $-path of length $ k $, we
have $(u, v)\in E $. In this paper, we study the structure of strong $ k $-transitive oriented …

One of the most interesting open problems of a digraph is Seymour's Second Neighborhood
Conjecture (SSNC), which asserts that every digraph D has a vertex v satisfying d++(v)≥ …

In 2006, Sullivan stated the conjectures:(1) every oriented graph has a vertex x such that
d++(x)≥ d−(x);(2) every oriented graph has a vertex x such that d++(x)+ d+(x)≥ 2 d−(x);(3) …

Let (D=(V, E)) be an oriented graph with minimum out‐degree δ+. For x∈ V (D), let d D+ x
and d D++ x be the out‐degree and second out‐degree of x in D, respectively. For a directed …

For a vertex xx of a digraph, d+(x) d^+(x) (d−(x) d^-(x), respectively) is the number of vertices
at distance 1 from (to, respectively) xx and d++(x) d^++(x) is the number of vertices at …

Abstract Sullivan stated the conjectures:(1) every oriented graph has a vertex x such that
d++(x)≥ d−(x) and (2) every oriented graph has a vertex x such that d++(x)+ d+(x)≥ 2 d−(x) …

Seymour's Second Neighborhood Conjecture asserts that every digraph has a vertex $ v $
whose second out-neighborhood $ N^{++}(v) $ is at least as large as its out-neighborhood …