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INDONESIA
Indonesian Journal of Combinatorics
Published by Indonesian Combinatorial Society
ISSN : 25412205     EISSN : -     DOI : -
Core Subject : Science,
Computer Science & IT Decision Sciences, Operations Research & Management
Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian Combinatorial Society (InaCombS), CGANT Research Group Universitas Jember (UNEJ), and Department of Mathematics Universitas Indonesia (UI).
Arjuna Subject : -
Articles 109 Documents
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The partition dimension of origami graphs and its barbell Luthfia Ayu Fakhira; Nur Wafiqoh Hadi; A. Asmiati; Dina Eka Nurvazly
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.2025.9.2.4

Abstract

The origami graph, On, n≥3, is a graph formed by a central cycle with origami folds, where each fold consists of two C3 cycles. The barbell origami graph, BOn for n≥3 is obtained by copying a On and connecting two graphs with a bridge. In this research, we determined the partition dimension of the origami graphs and its barbell.
Sum rules for permutations with fixed points involving Stirling numbers of the first kind Jean-Christophe Pain
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.2025.9.2.5

Abstract

We propose sum rules for permutations pn(k) of the ensemble {1,2,...,n} with k fixed points, in the form of partial sums of their moments. The corresponding identities involve Stirling numbers of the first kind s(q,r). Using a formula due to Vassilev-Missana and the Schlomlich expression of Stirling numbers, we also deduce sum rules for binomial coefficients. Connections with Bell numbers Bn are outlined.
Local edge antimagic chromatic number of join product of graphs Tita Khalis Maryati; Fawwaz Fakhrurrozi Hadiputra
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.2025.9.2.2

Abstract

Let f : V(G) \to [1,|V(G)|] be a bijective mapping of the vertex set of a graph G to the integers 1 through |V(G)|. A labeling f is defined as a local edge antimagic labeling if, for any two adjacent edges uv and vx in E(G), their weights satisfy wf(uv) ≠ wf(vx), where the weight of an edge uv is given by wf(uv) = f(u) + f(v). The weight wf induces a proper edge coloring on G. The local edge antimagic chromatic number of G, denoted χlea'(G), is the minimum number of colors required among all colorings induced by local edge antimagic labelings of G. In this paper, we investigate the local edge antimagic coloring of join product of graphs, particularly for independent sets, paths, and cycles.
Tripotent graph of finite rings Haval M. Mohammed Salih
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.1

Abstract

In this paper, we find the number of non-trivial tripotent elements for some finite rings, namely ℤn, H(?q), and ?q Cn. For this purpose, we find the general formula of them. Furthermore, we introduce the tri-potent graph of a finite ring R, denoted by Tri(R), where two distinct vertices x and y in R with a<b are adjacent if and only if a − b ∈ Tri(R). It is shown that the tri-potent graph is a bi-regular connected with girth at most 4. Also, the tri potent graph of ℤn is bipartite graph for some n.
Partition dimension of graphs with two bridges on rose graphs Puone Thahira Rachmani; A. Asmiati; Dian Kastika Syofyan; Aang Nuryaman
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.2

Abstract

The partition dimension of a graph G, denoted by pd(G) is a generalization of the metric dimension, in which the distinction between vertices is no longer based on a specific set of vertices, but rather on a partition of the vertex set of the graph. A partition is called a resolving partition if every vertex in the graph has a distinct distance vector representation with respect to each subset in the partition. The minimum cardinality of such a resolving partition is called the partition dimension  of the graph. This study focuses on the partition dimension of double bridge graphs constructed from a pair of rose graphs. It is shown that the partition dimension of the double bridge graph obtained from two rose graphs connected by two bridge edges is 4
Totally antimagic total labeling of helm and gear graphs Earl Baron Marzan Almanzor; Michael Kirby Briones Rodriguez
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.3

Abstract

A total labeling of a graph G is a bijection from the union of the vertex set and the edge set of G to the set {1,2,...,|V(G)|+|E(G)|}. Under a total labeling, the vertex-weight of a vertex is defined as the sum of its label and the labels of all edges incident to it. Similarly, the edge-weight of an edge is the sum of its label and the labels of its two end vertices. A total labeling is said to be edge-antimagic total if all the edge-weights are pairwise distinct, and vertex-antimagic total if all the vertex-weights are pairwise distinct. If a total labeling is edge-antimagic total and vertex-antimagic total at the same time, then it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph. In this paper, we show that helm graphs Hn and gear graphs Gn are totally antimagic total graphs.
A note on line and total directed superhypergraphs, line bidirected graphs, line multidirected graphs, and related structures Takaaki Fujita
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.4

Abstract

Hypergraphs extend classical graphs by allowing hyperedges to connect any nonempty subset of vertices, thereby capturing complex group-level relationships. Superhypergraphs advance this framework by introducing recursively nested powerset layers, enabling the representation of hierarchical and self-referential links among hyperedges. A line graph encodes the adjacencies between edges of an original graph by transforming each edge into a vertex and connecting two vertices if their corresponding edges share a common endpoint. A total graph incorporates both the vertices and edges of the original graph as its own vertices, with edges representing adjacency or incidence between these entities. Various extensions of these graph concepts exist that incorporate directional information, such as Directed Graphs, Bidirected Graphs, and Multidirected Graphs. In this paper, we investigate the notions of line graphs and total graphs within the settings of Directed HyperGraphs, Directed SuperHyperGraphs, Bidirected Graphs, and Multidirected Graphs.
On rainbow antimagic coloring and local edge antimagic coloring of graphs Tita Khalis Maryati; Fawwaz Fakhrurrozi Hadiputra
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.5

Abstract

Let G be a connected graph of order n. Let f: V(G) → {1,2,...,n} be a bijection and for every uv ∈ E(G) consider wf(uv) = f(u) + f(v) as a coloring of the edge. For a pair of vertices u and v, they are connected by a rainbow path if there exists a path from u to v such that the edges have pairwise distinct colors from wf. The bijection f: V(G) → {1,2,...,n} is a rainbow antimagic coloring if for every two vertices there exists a rainbow path. Meanwhile, that bijection f: V(G) → {1,2,...,n} is local edge antimagic coloring if every two adjacent edges have distinct weights. The rainbow antimagic connection number rac(G) and local edge antimagic chromatic number χ'lea(G) is the minimum number of distinct edge weights over all rainbow antimagic coloring and local edge antimagic coloring, respectively.We investigate the relationship between rac(G) and χ'lea(G). We prove χ'lea(G) ≤ rac(G) for all graphs and provide conditions for equality. Graphs with diameter at most 2 or satisfying rac(G) = Δ(G) achieve equality. We construct a family Ad with arbitrarily large diameter d where Δ(Ad) = χ'lea(Ad) = rac(Ad), and a family Hn = Kn,n - nK2 of diameter 3 where χ'lea(Hn) = rac(Hn) = 2n-3 > Δ(Hn). These results present hints to the full characterization of graphs G with χ'lea(G) = rac(G).
Prime and odd prime labelings of several graph classes Hafif Komarullah; Vira Hari Krisnawati; Kristiana Wijaya; Noor Hidayat
Indonesian Journal of Combinatorics Vol 10, No 1 (2026)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2026.10.1.6

Abstract

A prime labeling of a graph is an assignment of distinct integers to its vertices such that any two adjacent vertices are labeled with numbers that are relatively prime. An odd prime labeling is a variant in which the labels are restricted to odd integers while still preserving the coprimality condition. Motivated by the odd prime graph conjecture, which asserts that every prime graph is odd prime, we study prime and odd prime labelings on various classes of graphs. We construct explicit labeling functions and prove that comb graphs, disjoint unions of comb graphs, triangular book graphs, and modified triangular book graphs K1,1,n ⊙ 2Sm admit both prime and odd prime labelings. We further establish an odd prime labeling for torch graphs, extending a known prime labeling result for this class. Consequently, all graph families considered in this paper satisfy the odd prime graph conjecture. These results expand the collection of graphs known to admit odd prime labelings and provide additional evidence supporting the conjecture.

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