On distance irregular labeling of ladder graph and triangular ladder graph

Abstract

In this paper, we discussed graph labelings that the distance irregular labeling within which will be presented the results of the distance irregularity strength of ladder graph and triangular ladder graph. The distance irregular labeling on a graph G with v vertices is defined as an assignment λ : V → {1, 2, • • • , k} so that the weights calculated at vertices are distinct. The weight of a vertex x in G is defined as the sum of the labels of all the vertices adjacent to x (distance 1 from x), that is, wt(x) = Σ y∈N (x) λ(y). The distance irregularity strength of G, denoted by dis(G), is the minimum value of the largest label k over all such irregular assignments.

On Distance Vertex Irregular Total k-Labeling

“…Chartrand et al (1988) first introduced Irregular labeling in 1988, which developed very rapidly since then. Various types of irregular labeling such as VITL (Anholcer et al, 2009;Bača et al, 2007;Indriati et al, 2016;Baskoro et al, 2010), EITL (Anholcer and Palmer, 2012;) Indriati et al, 2013), totally ITL (Indriati et al, 2020;Marzuki et al, 2013), DVIL (Bong et al, 2017;Novindasari et al, 2016;Slamin, 2017;Sugeng et al, 2021;Susanto et al, 2022a;Susanto et al, 2022b), andDVITL (Wijayanti et al, 2021;Wijayanti et al, 2023). Wijayanti et al ( 2021) define the basic concept of DVITL and tdis(G) and also research some necessary and sufficient conditions for the existence of DVITL (Wijayanti et al, 2023) .…”

Non-inclusive and inclusive distance irregularity strength for the join product of graphs

“…A number of research results on non-inclusive and inclusive d-distance irregularity strengths have been found as seen in [3,4,11,13,14,15,16,17] when d = 1 and in [5,18] when d > 1.…”

On Distance Irregular Labeling of Disconnected Graphs

“…As a consequence of this property, he showed that some classes of graphs such as complete bipartite graphs, complete multipartite graphs, stars and trees containing vertex with at least two leaves, have no distance irregular labeling. Novindasari, Marjono and Abusini in [7] determined the distance irregularity strength of ladder graph and triangular ladder graph. Recently, in [2], Bong et al completed the results for the distance irregularity strength of C n and W n , for n ≡ 3, 4, 6, 7 (mod 8).…”