Degree sequence for k-arc strongly connected multiple digraphs - Yanmei Hong; Qinghai Liu (Journal of Inequalities and Applications, 2017)
Abstract Let D be a digraph on { v 1 , … , v n } $\{v_{1},…, v_{n}\}$ . Then the sequence { ( d + ( v 1 ) , d − ( v 1 ) ) , … , ( d + ( v n ) , d − ( v n ) ) } $\{ (d^{+}(v_{1}), d^{-}(v_{1})), …, (d^{+}(v_{n}), d^{-}(v_{n}))\}$ is called the degree sequence of D. For any given sequence of pairs of integers d = { ( d 1 + , d 1 − ) , … , ( d n + , d n − ) } $d=\{(d_{1}^{+}, d_{1}^{-}), …, (d_{n}^{+}, d_{n}^{-})\}$ , if there exists a k-arc strongly connected digraph D such that d is the degree sequence of D, then d is realizable and D is a realization of d. In this paper, characterizations for k-arc-connected realizable sequences and realizable sequences with arc-connectivity exactly k are given.