TY - GEN

T1 - Inclusive vertex irregular 1-distance labelings on triangular ladder graphs

AU - Utami, Budi

AU - Ariyanti, Kiki

AU - Utama, Suarsih

PY - 2018/10/17

Y1 - 2018/10/17

N2 - For a simple and connected graph G, the distance between two vertices u, v ϵ V (G), denoted by d(u, v), is the length of the shortest path connecting them. A vertex labeling λ: V (G) → {1, ⋯, k} is called an inclusive vertex irregular d-distance labeling if the weights of the vertices are distinct, where the weight of a vertex v is defined as the sum of the vertex label v and all vertex labels u such that d(u, v) ≤ d. The minimal value of the largest label k of all such labeling of G is called the inclusive d-distance irregularity strength of G and is denoted by disd0(G). Lower and upper bounds for disd0(G) have already been investigated for any graph G with d = 1. The value of dis10(G) for some classes of graphs, such as paths, cycles, complete graphs, and other related types of graphs, have also been determined in the literature. In this paper, we find an upper bound for dis10(G) for triangular ladder graphs Ln, with n ≡ 4 mod 5, n > 4, and the exact value for the rest of the cases with n ≥ 3.

AB - For a simple and connected graph G, the distance between two vertices u, v ϵ V (G), denoted by d(u, v), is the length of the shortest path connecting them. A vertex labeling λ: V (G) → {1, ⋯, k} is called an inclusive vertex irregular d-distance labeling if the weights of the vertices are distinct, where the weight of a vertex v is defined as the sum of the vertex label v and all vertex labels u such that d(u, v) ≤ d. The minimal value of the largest label k of all such labeling of G is called the inclusive d-distance irregularity strength of G and is denoted by disd0(G). Lower and upper bounds for disd0(G) have already been investigated for any graph G with d = 1. The value of dis10(G) for some classes of graphs, such as paths, cycles, complete graphs, and other related types of graphs, have also been determined in the literature. In this paper, we find an upper bound for dis10(G) for triangular ladder graphs Ln, with n ≡ 4 mod 5, n > 4, and the exact value for the rest of the cases with n ≥ 3.

KW - inclusive d-distance irregularity strength

KW - triangular ladder graph

KW - vertex labelling

UR - http://www.scopus.com/inward/record.url?scp=85056159821&partnerID=8YFLogxK

U2 - 10.1063/1.5062770

DO - 10.1063/1.5062770

M3 - Conference contribution

AN - SCOPUS:85056159821

T3 - AIP Conference Proceedings

BT - 8th Annual Basic Science International Conference

A2 - Karim, Corina

A2 - Azrianingsih, Rodliyati

A2 - Pamungkas, Mauludi Ariesto

A2 - Jatmiko, Yoga Dwi

A2 - Safitri, Anna

PB - American Institute of Physics Inc.

T2 - 8th Annual Basic Science International Conference: Coverage of Basic Sciences toward the World's Sustainability Challanges, BaSIC 2018

Y2 - 6 March 2018 through 7 March 2018

ER -