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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 4 Documents
 1 
Search results for , issue "Vol 7, No 1 (2023)" : 4 Documents clear
Local Strong Rainbow Connection Number of Corona Product Between Cycle Graphs Khairunnisa N. Afifah; Kiki A. Sugeng
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.2023.7.1.4

Abstract

A rainbow geodesic is a shortest path between two vertices where all edges are colored differently. An edge coloring in which any pair of vertices with distance up to d, where d is a positive integer that can be connected by a rainbow geodesic is called d-local strong rainbow coloring. The d-local strong rainbow connection number, denoted by lsrcd(G), is the least number of colors used in d-local strong rainbow coloring. Suppose that G and H are graphs of order m and n, respectively. The corona product of G and H, G ⊙ H, is defined as a graph obtained by taking a copy of G and m copies of H, then connecting every vertex in the i-th copy of H to the i-th vertex of G. In this paper, we will determine the lsrcd(Cm ⊙ Cn) for d=2 and d=3.
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.
On Ramsey (mK2,bPn)-minimal Graphs Nadia Nadia; Lyra Yulianti; Fawwaz Fakhrurrozi Hadiputra
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.2023.7.1.2

Abstract

Let G and H be two given graphs. The notation F→(G,H) means that any red-blue coloring on the edges of F will create either a red subgraph G or a blue subgraph H in F. A graph F is a Ramsey (G,H)-minimal graph if F satisfies two conditions: (1) F→(G,H), and (2) (F−e) ⇸ (G,H) for every e ∈ E(F). Denote ℜ(G,H) as the set of all (G,H)-minimal graphs. In this paper we prove that a tree T is not in ℜ(mK2,bPn) if it has a diameter of at least n(b+m−1)−1 for m,n,b≥2, furthermore we show that (b+m−1)Pn ∈ ℜ(mK2,bPn) for every m,n,b≥2. We also prove that for n≥3, a cycle on k vertices is in ℜ(mK2,bPn) if and only if k ∈ [n(b+m−2)+1, n(b+m−1)−1].
Γ-supermagic labeling of products of two cycles with cyclic groups Dalibor Froncek
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.2023.7.1.3

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 the sum of labels of all edges incident with any vertex x∈ V is equal to the same element μ ∈ Γ. A Z2mn-supermagic labeling of the Cartesian product of two cycles, Cm ℺ Cn for every m,n ≥ 3 was found by Froncek, McKeown, McKeown, and McKeown. In this paper we present a Zk-supermagic labeling of the direct and strong product by cyclic group Zk for any m,n ≥ 3.

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