TY - JOUR

T1 - The total vertex irregularity strength of generalized helm graphs and prisms with outer pendant edges

AU - Indriati, Diari

AU - Widodo,

AU - Wijayanti, Indah E.

AU - Ariyanti, Kiki

AU - Bača, Martin

AU - Semaničová-Feňovčíková, Andrea

PY - 2016/1/1

Y1 - 2016/1/1

N2 - For a simple graph G = (V,E) with the vertex set V and the edge set E, a vertex irregular total k-labeling f: V ∪E → {1, 2,…, k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x′, their weights wtf (x) = f(x) + ∑xy ∈E f(xy) and wtf (x′) = f(x′)+ ∑x ′y ′ ∈E f(x′y′) are distinct. A smallest positive integer k for which G admits a vertex irregular total k-labeling is defined as a total vertex irregularity strength of graph G, denoted by tvs(G). In this paper, we determine the exact value of the total vertex irregularity strength for generalized helm graphs and for prisms with outer pendant edges.

AB - For a simple graph G = (V,E) with the vertex set V and the edge set E, a vertex irregular total k-labeling f: V ∪E → {1, 2,…, k} is a labeling of vertices and edges of G in such a way that for any two different vertices x and x′, their weights wtf (x) = f(x) + ∑xy ∈E f(xy) and wtf (x′) = f(x′)+ ∑x ′y ′ ∈E f(x′y′) are distinct. A smallest positive integer k for which G admits a vertex irregular total k-labeling is defined as a total vertex irregularity strength of graph G, denoted by tvs(G). In this paper, we determine the exact value of the total vertex irregularity strength for generalized helm graphs and for prisms with outer pendant edges.

UR - http://www.scopus.com/inward/record.url?scp=84962367741&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84962367741

VL - 65

SP - 14

EP - 26

JO - Australasian Journal of Combinatorics

JF - Australasian Journal of Combinatorics

SN - 1034-4942

IS - 1

ER -