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Indonesian Journal of Combinatorics

ijc
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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 103 Documents

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Some methods for constructing some classes of graceful uniform trees I Nengah Suparta; I Dewa Made Agus Ariawan
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

A tree T(V, E) is graceful if there exists an injective function f from the vertex set V(T) into the set {0, 1, 2, ..., ∣V∣ − 1} which induces a bijective function fʹ from the edge set E(T) onto the set {1, 2, ..., ∣E∣}, with fʹ(uv) = ∣f(u) − f(v)∣ for every edge {u, v} ∈ E. Motivated by the conjecture of Alexander Rosa (see) saying that all trees are graceful, a lot of works have addressed gracefulness of some trees. In this paper we show that some uniform trees are graceful. This results will extend the list of graceful trees.

Some results on cordiality labeling of generalized Jahangir graph Roslan Hasni; S. Matarneh; Almothana Azaizeh
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

In this paper we consider the cordiality of a generalized Jahangir graph $J_{n,m}$. We give sufficient condition for $J_{n,m}$ to admit (or not admit) the prime cordial labeling, product cordial labeling and total product cordial labeling.

Graceful labeling on torch graph Jona Martinus Manulang; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G be a graph with vertex set V = V(G) and edge set E = E(G). An injective function f : V → {0, 1, 2, ..., ∣E∣} is called graceful labeling if f induces a function f * (uv) = ∣f(u) − f(v)∣ which is a bijection from E(G) to the set {1, 2, 3, ..., ∣E∣}. A graph which admits a graceful labeling is called a graceful graph. In this paper, we show that torch graph On is a graceful graph.

Exclusive graphs: a new link among labelings Rikio Ichishima; Francesc A. Muntaner-Batle; Akito Oshima
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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.

On the subdivided thorn graph and its metric dimension Lyra Yulianti; Narwen Narwen; Sri Hariyani
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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 Dina Eka Nurvazly; Jona Martinus Manulang; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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 Johan Kok; Sudev Naduvath; Muhammad Kamran Jamil
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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 Antonius Cahya Prihandoko; D. Dafik; Ika Hesti Agustin
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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 Dalibor Froncek; O'Neill Kingston
Indonesian Journal of Combinatorics Vol 3, No 1 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

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.

Certain topological indices and polynomials for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph Salma Kanwal; Mariam Imtiaz; Ayesha Manzoor; Nazeeran Idrees; Ammara Afzal
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.

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