TY - JOUR

T1 - Local inclusive distance vertex irregular graphs

AU - Sugeng, Kiki Ariyanti

AU - Silaban, Denny Riama

AU - Bača, Martin

AU - Semaničová-Feňovčíková, Andrea

N1 - Funding Information:
Funding: This research has supported by PUTI KI-Universitas Indonesia 2020 Research Grant No. NKB-779/UN2.RST/HKP.05.00/2020. This work was also supported by the Slovak Research and Development Agency under the contract No. APVV-19-0153 and by VEGA 1/0233/18.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/7/2

Y1 - 2021/7/2

N2 - Let G = (V, E) be a simple graph. A vertex labeling f: V(G) → {1, 2, …, k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x, y ∈ V(G) their weights are distinct, where the weight of a vertex x ∈ V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d = 1 and determine the precise values of the corresponding graph invariant for certain families of graphs.

AB - Let G = (V, E) be a simple graph. A vertex labeling f: V(G) → {1, 2, …, k} is defined to be a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of a graph G if for any two adjacent vertices x, y ∈ V(G) their weights are distinct, where the weight of a vertex x ∈ V(G) is the sum of all labels of vertices whose distance from x is at most d (respectively, at most d but at least 1). The minimum k for which there exists a local inclusive (respectively, non-inclusive) d-distance vertex irregular labeling of G is called the local inclusive (respectively, non-inclusive) d-distance vertex irregularity strength of G. In this paper, we present several basic results on the local inclusive d-distance vertex irregularity strength for d = 1 and determine the precise values of the corresponding graph invariant for certain families of graphs.

KW - (inclusive) distance vertex irregular labeling

KW - Local (inclusive) distance vertex irregular labeling

UR - http://www.scopus.com/inward/record.url?scp=85111259348&partnerID=8YFLogxK

U2 - 10.3390/math9141673

DO - 10.3390/math9141673

M3 - Article

AN - SCOPUS:85111259348

VL - 9

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 14

M1 - 1673

ER -