TY - JOUR

T1 - Note on in-antimagicness and out-antimagicness of digraphs

AU - Arumugam, S.

AU - Bača, Martin

AU - Marr, Alison

AU - Semaničová-Feňovčíková, Andrea

AU - Sugeng, Kiki Ariyanti

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - (a, d)-vertex-in-antimagic graph

KW - (a, d)-vertex-out-antimagic graph

KW - 05C20

KW - 05C78

KW - In-regular digraph

KW - Out-regular digraph

UR - http://www.scopus.com/inward/record.url?scp=85087438965&partnerID=8YFLogxK

U2 - 10.1080/09720529.2020.1758366

DO - 10.1080/09720529.2020.1758366

M3 - Article

AN - SCOPUS:85087438965

JO - Journal of Discrete Mathematical Sciences and Cryptography

JF - Journal of Discrete Mathematical Sciences and Cryptography

SN - 0972-0529

ER -