Note on in-antimagicness and out-antimagicness of digraphs

S. Arumugam, Martin Bača, Alison Marr, Andrea Semaničová-Feňovčíková, Kiki Ariyanti Sugeng

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalJournal of Discrete Mathematical Sciences and Cryptography
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • (a, d)-vertex-in-antimagic graph
  • (a, d)-vertex-out-antimagic graph
  • 05C20
  • 05C78
  • In-regular digraph
  • Out-regular digraph

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