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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Fawwaz Fakhrurrozi Hadiputra
Master Program of Mathematics, Institut Teknologi Bandung, Bandung - Indonesia
Electrical & Electronics Engineering

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Further results on local inclusive distance vertex irregularity strength of graphs Fawwaz Fakhrurrozi Hadiputra; Eunike Setiawan; Tita Khalis Maryati; Denny Riama Silaban
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2023.11.1.21

Abstract

Let G = (V, E) be a simple undirected graph. A labeling f : V(G)→{1, …, k} is a local inclusive d-distance vertex irregular labeling of G if every adjacent vertices x, y ∈ V(G) have distinct weights, with the weight w(x),x ∈ V(G) is the sum of every labels of vertices whose distance from x is at most d. The local inclusive d-distance vertex irregularity strength of G, lidis(G), is the least number k for which there exists a local inclusive d-distance vertex irregular labeling of G. In this paper, we prove a conjecture on the local inclusive d-distance vertex irregularity strength for d = 1 for tree and we generalize the result for block graph using the clique number. Furthermore, we present several results for multipartite graphs and we also observe the relationship with chromatic number.
Co-Authors Denny Riama Silaban Eunike Setiawan Tita Khalis Maryati