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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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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
Γ-supermagic labeling of products of two cycles with dihedral groups Froncek, Dalibor
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2025.9.1.1

Abstract

A  Γ-supermagic labeling of a graph G=(V,E) is a bijection from E to a group Γ of order |E| such that for every vertex x∈V a product of labels of all edges incident with x is equal to the same element µ∈Γ.  A Γ-supermagic labeling of the Cartesian product of two cycles, CmℹCn for every m,n≥3 of the same parity was found recently [5, 6] for all Abelian groups of order 2mn. In this paper we present a Dk-supermagic labeling of the Cartesian, direct, and strong product by dihedral group Dk for any m,n≥3.
Local edge antimagic coloring for chain of path and cycle Walfried, Yosua; Chandra, Ivana Joice; Silaban, Denny Riama
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2025.9.1.2

Abstract

Let G=(V,E) be a simple connected graph with vertex set V and edge set E. A local edge antimagic labeling of G is a bijection f:V (G)→{1, 2, 3, ... , |V(G)|} where the weights of any two adjacent edges of G are distinct. The weight of an edge uv is defined as w(uv) = f(u)+f(v). By assigning the color w(uv) to each edge uv ∈ E(G), we obtain a proper local edge antimagic coloring of G. The minimum number of colors required for edge coloring induced by the local edge antimagic labeling is called a local antimagic chromatic index of G. In this article, we give the exact value of the local antimagic chromatic index for the chain of path and cycle graphs.
The number of spanning trees of cyclic snakes Barrientos, Christian
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.9.1.3

Abstract

A cyclic snake is a connected graph formed by connecting, by means of vertex amalgamation, a certain number of copies of the cycle Cn, in such a way that the i-th copy of Cn is connected with the (i+1)-th copy, resulting in a graph with maximum degree 4. Spanning trees of this type of graph can be easily found, but finding the number of nonisomorphic spanning trees of a given cyclic snake is a more challenging problem. In this work, we investigate the number of cyclic snakes formed with k copies of Cn, the number of spanning trees of any given cyclic snake. We also classified these trees according to their diameters. Finally, we study the morphology of the trees associated to the snakes where the distance between cut-vertices is a constant.
Seidel spectrum for splitting V-vertex join and S-vertex join of graphs Ramane, Harishchandra S.; Patil, Daneshwari D.
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.9.1.4

Abstract

Splitting V-vertex join and S-vertex join of graphs are the graph structures obtained from splitting graph of a graph. Present work concentrates on the study of Seidel spectrum for the vertex join structures considered.
Games of Nim with Dynamic Restrictions Mizugaki, Keita; Takahashi, Shoei; Manabe, Hikaru; Murakami, Aoi; Miyadera, Ryohei
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.9.1.5

Abstract

The authors present formulas for the previous player’s winning positions of two variants of restricted Nim. In both of these two games, there is one pile of stones, and in the first variant, we investigate the case that in k-th turn, you can remove f(k) stones at most, where f is a function whose values are natural numbers. In the second variant, there are two kinds of stones. The Type 1 group consists of stones with the weight of one, and the Type 2 group consists of stones with the weight of two. When the total weight of stones is a, you can remove stones whose total weight is equal to or less than ⌊a/2⌋
On Coloring of Fractional Powers of Star, Wheel, Friendship, and Fan Graphs Hafizh, Farisan; Maulana, Muhammad Rayhanafraa Gibran; Vienny, Citius; Joyosumarto, Bisma Rohpanca; Sugeng, Kiki A.
Indonesian Journal of Combinatorics Vol 9, No 1 (2025)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2024.9.1.6

Abstract

Let G be a simple, connected, and undirected graph. For m, n ∈ ℕ, the fractional power Gm/n = (G1/n)m of G is constructed by taking the n-subdivision of G (replacing each edge by a path of length n), and then raising the resulting graph to the m-th power (connecting any two distinct vertices with distance at most m).Let ω(G) be a clique number of G and χ(G) be the chromatic number of G. Iradmusa formulated a closed form for the clique number of Gm/n(ω(Gm/n)) and conjectured that χ(Gm/n) = ω(Gm/n) for every m, n ∈ ℕ where m/n < 1 and ∆(G) ≥ 3. The conjecture is true for certain special cases, such as paths, cycles and complete graphs. However, Hartke et. al. found a counterexample of the conjecture, that is the graph G = C3 ↆ K2 when m = 3 and n = 5. In this paper, we aim to prove that the conjecture is true for some classes of graphs that is not yet addressed. We prove that χ(Gm/n) = ω(Gm/n) for star, wheel, friendship, and fan graphs G.

Page 10 of 10 | Total Record : 98

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