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

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Distance antimagic labelings of product graphs Risma Yulina Wulandari; Rinovia Simanjuntak
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.2023.11.1.9

Abstract

A graph G is distance antimagic if there is a bijection f : V(G)→{1, 2, …, |V(G)|} such that for every pair of distinct vertices x and y applies w(x)≠w(y), where w(x)=Σ z ∈ N(x)f(z) and N(x) is the neighbourhood of x, i.e., the set of all vertices adjacent to x. It was conjectured that a graph is distance antimagic if and only if each vertex in the graph has a distinct neighbourhood. In this paper, we study the truth of the conjecture by posing sufficient conditions and constructing distance antimagic product graphs; the products under consideration are join, corona, and Cartesian.
On (F, H)-simultaneously-magic labelings of graphs Yeva Fadhilah Ashari; A.N.M. Salman; Rinovia Simanjuntak; Andrea Semaničová-Feňovčíková; Martin Baca
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.2023.11.1.5

Abstract

A simple graph G(V, E) admits an H-covering if every edge in G belongs to a subgraph of G isomorphic to H. In this case, G is called H-magic if there exists a bijective function f : V ∪ E → {1, 2, …, |V|+|E|}, such that for every subgraph H′ of G isomorphic to H, wtf(H′) =  Σv ∈ V(H′)f(v)+ Σe ∈ E(H′)f(e) is constant. Moreover, G is called H-supermagic if f : V(G)→{1, 2, …, |V|}. This paper generalizes the previous labeling by introducing the (F, H)-sim-(super) magic labeling. A graph admitting an F-covering and an H-covering is called (F, H)-sim-(super) magic if there exists a function f that is F-(super)magic and H-(super)magic at the same time. We consider such labelings for two product graphs: the join product and the Cartesian product. In particular, we establish a sufficient condition for the join product G + H to be (K2 + H, 2K2 + H)-sim-supermagic and show that the Cartesian product G × K2 is (C4, H)-sim-supermagic, for H isomorphic to a ladder or an even cycle. Moreover, we also present a connection between an α-labeling of a tree T and a (C4, C6)-sim-supermagic labeling of the Cartesian product T × K2.
A note on vertex irregular total labeling of trees Faisal Susanto; Rinovia Simanjuntak; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 7, No 1 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.1.1

Abstract

The total vertex irregularity strength of a graph G=(V,E) is the minimum integer k so that there is a mapping from V ∪ E to the set {1,2,...,k} so that the vertex-weights (i.e., the sum of labels of a vertex together with the edges incident to it) are all distinct. In this note, we present a new sufficient condition for a tree to have total vertex irregularity strength ⌈(n1+1)/2⌉, where n1 is the number of vertices of degree one in the tree.
Co-Authors A.N.M. Salman Andrea Semaničová-Feňovčíková Edy Tri Baskoro Faisal Susanto Martin Baca Risma Yulina Wulandari Yeva Fadhilah Ashari