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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).
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Articles 98 Documents
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On inclusive distance vertex irregularity strength of book graph Wahyu, Ria Ammelia; Santoso, Kiswara Agung; Slamin, Slamin
Indonesian Journal of Combinatorics Vol 7, No 2 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.2.4

Abstract

The concept of distance vertex irregular labeling of graphs was introduced by Slamin in 2017. The distance vertex irregular labeling on a graph G with v vertices is defined as an assignment λ : V → {1, 2, ..., k} so that the weights calculated at vertices are distinct. The weight of a vertex x in G is defined as the sum of the labels of all the vertices adjacent to x (distance 1 from x). The distance vertex irregularity strength of graph G, denoted by dis(G), is defined as the minimum value of the largest label k over all such irregular assignments. Bong, Lin and Slamin generalized the concept to inclusive and non-inclusive distance irregular labeling. The difference between them depends on the way to calculate the weight on the vertex whether the vertex label we calculate its weight is included or not. The inclusive distance vertex irregularity strength of G, is defined as the minimum of the largest label k over all such inclusive irregular assignments. In this paper, we determine the inclusive distance vertex irregularity strength of some particular classes of graphs such as book graph.
Numbers of Weights of Convex Quadrilaterals in Weighted Point Sets Sakai, Toshinori; Matsumoto, Satoshi
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.2024.8.1.1

Abstract

Let ℘n denote the family of sets of points in general position in the plane each of which is assigned a different number, called a weight, in {1,2,...,n}. For P∈℘n and a polygon Q with vertices in P, we define the weight of Q as the sum of the weights of its vertices and denote by Wk(P) the set of weights of convex k-gons with vertices in P∈℘n. Let fk(n) = minP∈℘n |Wk(P)|. It is known that n-5 ≤ f4(n) ≤ 2n-9 for n≥7. In this paper, we show that f4(n)≥ 4n/3-7.
On the generating graph of a finite group Mohammed Salih, Haval M.
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.2024.8.1.3

Abstract

In this paper, we study the generating graph for some finite groups which are semi-direct product ℤn ⋊ ℤm (direct product ℤn × ℤm) of cyclic groups ℤn and ℤm. We show that the generating graphs of them are regular (bi-regular, tri-regular) connected graph with diameter 2 and girth 3 if n and m are prime numbers. Several graph properties are obtained. Furthermore, the probability that 2-randomly elements that generate a finite group G is P(G) = |{(a,b) ∈ G×G|G=❬a,b❭}|/|G|2. We find the general formula for P(G) of given groups. Our computations are done with the aid of GAP and the YAGs package.
When is the maximal graph of a non-quasi-local atomic domain connected? Visweswaran, Subramanian
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.2024.8.1.4

Abstract

In this paper, with any atomic domain R which admits at least two maximal ideals, we associate an undirected graph denoted by ???(R) whose vertex set is I(R)={Rπ | π∈ Irr(R)\J(R)} (where Irr(R) is the set of all irreducible elements of R and J(R) is the Jacobson radical of R) and distinct Rπ, Rπ' ∈ I(R) are adjacent if and only if Rπ + Rπ' ⊆ M for some maximal ideal M of R. We call ???(R) as the maximal graph of R. We denote the set of all maximal ideals of R by Max(R). In this paper, some necessary (respectively, sufficient) conditions on Max(R) are provided such that ???(R) is connected. Also, in this paper, in some cases, a necessary and sufficient condition is determined so that ???(R) is connected.
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.
On Ramsey numbers for trees versus fans of even order Sherlin, Intan; Saputro, Suhadi Wido; Baskoro, Edy Tri; Oktariani, Finny
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.2024.8.1.2

Abstract

Given two graphs G and H. The graph Ramsey number R(G, H) is the least natural number r such that for every graph F on r vertices, either F contains a copy of G or F̅ contains a copy of H. A vertex v is called a dominating vertex in a graph G if it is adjacent to all other vertices of G. A wheel Wm is a graph consisting one dominating vertex and m other vertices forming a cycle. A fan graph F1,m is a graph formed from a wheel Wm by removing one cycle-edge. In this paper, we consider the graph Ramsey number R(Tn,F1,m) of a tree Tn versus a fan F1,m. The study of R(Tn,F1,m) has been initiated by Li et. al. (2016) where Tn is a star, and continued by Sherlin et. al. (2023) for Tn which is not a star and fan F1,m with even m ≤ 8. This paper will give the graph Ramsey numbers R(Tn,F1,m) for odd m ≤ 8.
Family of Graphs with Partition Dimension Three Haryeni, Debi Oktia; Baskoro, Edy Tri; Saputro, Suhadi Wido
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.1

Abstract

The characterization of all connected graphs of order n ≥3 with partition dimension 2, n−1 or n has been completely done. Additionally, all connected graphs of order n≥9 with partition dimension n−2 and graphs of order n≥11 with partition dimension n−3 have been characterized as well. However, the characterization of all connected graphs with partition dimension 3 is an open problem. In this paper, we construct many families of disconnected as well as connected graphs with partition dimension 3 by generalizing the concept of the partition dimension so that it can be applied to disconnected graphs.
Characteristic Polynomial of Antiadjacency Matrix of Several Classes of Graph Join Ataupah, Anthony Arthur; Putra, Ganesha Lapenangga
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.2

Abstract

Suppose G is a simple and undirected graph. The adjacency matrix of graph G, denoted by A(G) is a square matrix that representing graph G based on the adjacency of vertices on G, denoted by A(G). The antiadjacency matrix of graph G is a matrix B(G)=J−A(G) where J is an n×n matrixwith all the entries equal to 1. This paper deliver the result of study about the characteristic polynomial of antiadjacency matrix of several graph join, such as multipartite graph, windmill graph, and cone graph.
Reflexive Edge Strength on Slanting Ladder Graph and Corona of Centipede and Null Graph Ispriyanto, Mochamad Raffli; Indriati, Diari; Utomo, Putranto Hadi
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.3

Abstract

Assume G is a graph that is simple, undirected, and connected. If every edge label is a positive integer in the range 1 to ke, and every vertex label is a non-negative even number from 0 to 2kv, then a graph G is considered to have an edge irregular reflexive k-labeling, where k is defined as the maximum of ke and 2kv. The edge weight wt(ab) in the graph G, for the labeling λ, is defined as the function wt applied to the edge ab. The symbol res(G) denotes the reflexive edge strength, which is the largest label of the smallest k. The results of this research are as follows: res(SLm) for m≥2 is ⌈(3m−3)/3⌉ for 3m−3 ≢ 2, 3 (mod 6), and ⌈(3m−3)/3⌉+1 for 3m−3 ≡ 2, 3 (mod 6). res(Cpn ⊙ Nm) for n≥2, m≥1 is ⌈(2nm+2n−1)/3⌉ for 2nm+2n−1 ≢ 2, 3 (mod 6), and ⌈(2nm+2n−1)/3⌉+1 for 2nm+2n−1 ≡ 2, 3 (mod 6).
Zonal Labeling of Graphs Barrientos, Christian; Minion, Sarah
Indonesian Journal of Combinatorics Vol 8, No 2 (2024)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.8.2.4

Abstract

A planar graph is said to be zonal when is possible to label its vertices with the nonzero elements of ℤ3, in such a way that the sum of the labels of the vertices on the boundary of each zone is 0 in ℤ3. In this work we present some conditions that guarantee the existence of a zonal labeling for a number of families of graphs such as unicyclic and outerplanar, including the family of bipartite graphs with connectivity at least 2 whose stable sets have the same cardinality; additionally, we prove that when any edge of a zonal graph is subdivided twice, the resulting graph is zonal as well. Furthermore, we prove that the Cartesian product G × P2 is zonal, when G is a tree, a unicyclic graph, or certain variety of outerplanar graphs. Besides these results, we determine the number of different zonal labelings of the cycle Cn.

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