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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 6 Documents
 1 
Search results for , issue "Vol 8, No 2 (2024)" : 6 Documents clear
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.
Strong 3-Rainbow Indexes of Closed Helm Graphs Nugrahani, Calista Suci; Constantine, Christian; Salman, A. N. M.
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.2024.8.2.5

Abstract

Let G be a nontrivial, edge-colored, and connected graph of order m≥3 where adjacent edges may have the same color. A tree T in graph G is called a rainbow tree if all the edges in T have different colors. For S⊆V(G), the Steiner distance sd(S) of S is the minimum size of a tree in G containing S. Let k be an integer with 2≤k≤m. An edge-coloring in G is a strong k-rainbow coloring if for every set S of k vertices of G, there exists a rainbow tree of size sd(S) in G containing S. In this paper, we study the strong 3-rainbow index (srx3) of Closed Helm graph. We also determine the srx3 of Closed Helm graph.
Locating Chromatic Number for Corona Operation of Path and Cycle Hamzah, Nur; Asmiati, A.; Amansyah, Wahyu Dwi
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.2024.8.2.6

Abstract

The locating chromatic number (lcn) of a graph is a part of discrete mathematic research, there is no general theorem for determining the lcn of any graph. The corona operation of Pn and Cm, denoted by Pn⊙Cm is defined as the graph obtained by taking one copy of Pn and |V(Pn)| copies of Cm and then joining all the vertices of the kth-copy of Cm with the kth-vertex of Pn. In this paper, we discuss the lcn for the corona operation of path and cycle. The lcn of (Pn⊙C3) is 5 for 3 ≤n< 7 and 6 for n≥7. Moreover, the lcn of (Pn⊙C4) is 5 for 3≤n< 6 and 6 for n≥6

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