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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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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.
D-antimagic labelings arising from completely separating systems Wulandari, Risma Yulina; Simanjuntak, Rinovia; Saputro, Suhadi Wido
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): 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.2025.13.2.2

Abstract

Let D be a non-empty subset of the distance set {0,1,…, diam(G)}. A graph G is D-antimagic if there exists a bijection f:V(G)→{1,2,…,|V(G)|} such that for every pair of distinct vertices x and y, wD(x) ≠ wD(y), where wD(x) = Σz∈ND(x)f(z) is the D-weight of x and ND(x) = {z|d(x,z)∈D} is the D-neighbourhood of x. It was conjectured that a graph G is D-antimagic if and only if each vertex in G has a distinct D-neighborhood. A completely separating system (CSS) in the finite set {1,2,…,n} is a collection ? of subsets of {1,2,…,n} in which for each pair a≠b∈{1,2,…,n}, there exist A,B∈? such that a∈A−B and b∈B−A.In this paper, we provide evidence to support the conjecture mentioned earlier by using Roberts' completely separating systems to define D-antimagic labelings for certain graphs. In particular, we show that if G and H are D-antimagic graphs with labelings constructed from Roberts' CSS, then the vertex-deleted subgraph, G−{v} and the vertex amalgamation of G and H are also D-antimagic. Additionally, we partially answer an open problem of Simanjuntak et al. (2021) by constructing {1}-antimagic labelings for some disjoint unions of paths.
Co-Authors Farhan, Mohammad Hadiputra, Fawwaz Fakhrurrozi Mukayis, Mukayis Simanjuntak, Rinovia Tita Khalis Maryati Wulandari, Risma Yulina