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All Journal Electronic Journal of Graph Theory and Applications (EJGTA) Indonesian Journal of Combinatorics
Saputro, Suhadi Wido
Institut Teknologi Bandung
Computer Science & IT Decision Sciences, Operations Research & Management Electrical & Electronics Engineering

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Journal : Indonesian Journal of Combinatorics

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Local inclusive distance antimagic coloring of graphs Hadiputra, Fawwaz Fakhrurrozi; Farhan, Mohammad; Mukayis, Mukayis; Saputro, Suhadi Wido; Maryati, Tita Khalis
Indonesian Journal of Combinatorics Vol 8, No 1 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.1.5

Abstract

For a simple graph G, a bijection f : V(G) → [1,|V (G)|] is called as a local inclusive distance antimagic (LIDA) labeling of G if w(u) ≠ w(v) for every two adjacent vertices u,v ∈ V(G) with w(u) = ∑x∈N [u] f(x). A graph G is said to be local inclusive distance antimagic (LIDA) graph if it admits a LIDA labeling. The function w induced by f also can be seen as a proper vertex coloring of G. The local inclusive distance antimagic (LIDA) chromatic number of G, denoted by χlida(G), is the minimum number of colors taken over all proper vertex colorings induced by LIDA labelings of G. In this paper, we study a LIDA labeling of simple graph. We provide some basic properties of LIDA labeling for any simple graphs. The LIDA chromatic number of certain multipartite graphs, double stars, subdivision of graphs and join product of graphs with K1 are also investigated. We present an upper bound for graphs obtained from subdivision of super edge-magic total graphs. Furthermore, we present some new open problems.
Outer multiset dimension of joined graphs Pervaiz, Hassan; Simanjuntak, Rinovia; Saputro, Suhadi Wido
Indonesian Journal of Combinatorics Vol 9, No 2 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2025.9.2.1

Abstract

The outer multiset dimension of graph G, dimms(G), is the cardinality of the smallest subset S of vertices that uniquely recognizes each vertex outside S by using the multiset of distances between the vertex and the vertices in S. In 2023, Klavzar, Kuziak, and Yero proved that the only graphs with the largest outer multiset dimension, that is, one less than their order, are regular graphs of diameter at most 2. This paper considers the outer multiset dimensions of non-regular graphs of diameter 2 obtained from the join product, in particular, stars, wheels, generalized wheels, windmills, fans, and generalized fans. 
Co-Authors Farhan, Mohammad Hadiputra, Fawwaz Fakhrurrozi Mukayis, Mukayis Pervaiz, Hassan Simanjuntak, Rinovia Tita Khalis Maryati Wulandari, Risma Yulina