Note on in-antimagicness and out-antimagicness of digraphs

• Published in: Journal of discrete mathematical sciences & cryptography Vol. 25; no. 6; pp. 1603 - 1611
• Main Authors: Arumugam, S., Bača, Martin, Marr, Alison, Semaničová-Feňovčíková, Andrea, Sugeng, Kiki Ariyanti
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 18.08.2022
• Subjects: (a, d)-vertex-in-antimagic graph; (a, d)-vertex-out-antimagic graph; In-regular digraph; Out-regular digraph
• ISSN: 0972-0529; 2169-0065
• DOI: 10.1080/09720529.2020.1758366

A digraph D is called (a, d)-vertex-in-antimagic ((a, d)-vertex-out-antimagic) if it is possible to label its vertices and arcs with distinct numbers from the set {1, 2, ... ,|V(D)|+|A(D)|} such that the set of all in-vertex-weights (out-vertex-weights) form an arithmetic sequence with initial term a and a common difference d, where a > 0, d ≥ 0 are integers. The in-vertex-weight (out-vertex-weight) of a vertex n ϵ V(D) is defined as the sum of the vertex label and the labels of arcs ingoing (outgoing) to n. Moreover, if the smallest numbers are used to label the vertices of D such a graph is called super. In this paper we will deal with in-antimagicness and out-antimagicness of in-regular and out-regular digraphs.