Indonesian Journal of Combinatorics
ISSN : 25412205     EISSN : -
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).
Articles 6 Documents
Search results for , issue " Vol 3, No 1 (2019)" : 6 Documents clear
Exclusive graphs: a new link among labelings Ichishima, Rikio; Muntaner-Batle, Francesc A.; Oshima, Akito
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.1

Abstract

In this paper, we define a strongly felicitous graph to be lower-exclusive, upper-exclusive and exclusive depending on different restrictions for the vertex labels. With these new concepts, we show that the union of finite collection of strongly felicitous graphs, a lower-exclusive one and an upper-exclusive one results in a strongly felicitous graph. We also introduce the concept of decompositional graphs. By means of this, we provide some results involving the cartesian products of exclusive graphs.
A note on the metric dimension of subdivided thorn graphs Yulianti, Lyra; Narwen, Narwen; Hariyani, Sri
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.4

Abstract

For some ordered subset W = {w1, w2, ⋯, wt} of vertices in connected graph G, and for some vertex v in G, the metric representation of v with respect to W is defined as the t-vector r(v∣W) = {d(v, w1), d(v, w2), ⋯, d(v, wt)}. The set W is the resolving set of G if for every two vertices u, v in G, r(u∣W) ≠ r(v∣W). The metric dimension of G, denoted by dim(G), is defined as the minimum cardinality of W. Let G be a connected graph on n vertices. The thorn graph of G, denoted by Th(G, l1, l2, ⋯, ln), is constructed from G by adding li leaves to vertex vi of G, for li ≥ 1 and 1 ≤ i ≤ n. The subdivided-thorn graph, denoted by TD(G, l1(y1), l2(y2), ⋯, ln(yn)), is constructed by subdividing every li leaves of the thorn graph of G into a path on yi vertices. In this paper the metric dimension of thorn of complete graph, dim(Th(Kn, l1, l2, ⋯, ln)), li ≥ 1 are determined, partially answering the problem proposed by Iswadi et al . This paper also gives some conjectures for the lower bound of dim(Th(G, l1, l2, ⋯, ln)), for arbitrary connected graph G. Next, the metric dimension of subdivided-thorn of complete graph, dim(TD(Kn, l1(y1), l2(y2), ⋯, ln(yn)) are determined and some conjectures for the lower bound of dim(Th(G, l1(y1), l2(y2), ⋯, ln(yn)) for arbitrary connected graph G are given.
The oriented chromatic number of edge-amalgamation of cycle graph Nurvazly, Dina Eka; Manulang, Jona Martinus; Sugeng, Kiki A.
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.5

Abstract

An oriented k − coloring of an oriented graph G⃗ is a partition of V(G⃗) into k color classes such that no two adjacent vertices belong to the same color class, and all the arcs linking the two color classes have the same direction. The oriented chromatic number of an oriented graph G⃗ is the minimum order of an oriented graph H⃗ to which G⃗ admits a homomorphism to H⃗. The oriented chromatic number of an undirected graph G is the maximum oriented chromatic number of all possible orientations of the graph G. In this paper, we show that every edge amalgamation of cycle graphs, which also known as a book graph, has oriented chromatic number less than or equal to six.
Chromatic Zagreb indices for graphical embodiment of colour clusters Kok, Johan; Naduvath, Sudev; Jamil, Muhammad Kamran
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.6

Abstract

For a colour cluster C = (C1, C2, C3, …, Cℓ), where Ci is a colour class such that ∣Ci∣ = ri, a positive integer, we investigate two types of simple connected graph structures G1C, G2C which represent graphical embodiments of the colour cluster such that the chromatic numbers χ(G1C) = χ(G2C) = ℓ and $\min\{\varepsilon(G^{C}_1)\}=\min\{\varepsilon(G^{C}_2)\} =\sum\limits_{i=1}^{\ell}r_i-1$, and ɛ(G) is the size of a graph G. In this paper, we also discuss the chromatic Zagreb indices corresponding to G1C, G2C.
Implementation of super H-antimagic total graph on establishing stream cipher Prihandoko, Antonius Cahya; Dafik, D.; Agustin, Ika Hesti
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.2

Abstract

This paper is aimed to study the use of super (a, d)-H antimagic total graph on generating encryption keys that can be used to establish a stream cipher. Methodology to achieve this goal was undertaken in three steps. First of all the existence of super (a, d)-H-antimagic total labeling was proven. At the second step, the algorithm for utilizing the labeling to construct a key stream was developed, and finally, the mechanism for applying the key to establish a stream cipher was constructed. As the result, according to the security analysis, it can be shown that the developed cryptographic system achieve a good security.
Decomposition of complete graphs into connected unicyclic graphs with eight edges and pentagon Froncek, Dalibor; Kingston, O'Neill
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2019.3.1.3

Abstract

A G-decomposition of the complete graph Kn is a family of pairwise edge disjoint subgraphs of Kn, all isomorphic to G, such that every edge of Kn belongs to exactly one copy of G. Using standard decomposition techniques based on ρ-labelings, introduced by Rosa in 1967, and their modifications we show that each of the ten non-isomorphic connected unicyclic graphs with eight edges containing the pentagon decomposes the complete graph Kn whenever the necessary conditions are satisfied.

Page 1 of 1 | Total Record : 6