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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 7 Documents
 1 
Search results for , issue "Vol 4, No 1 (2020)" : 7 Documents clear
On additive vertex labelings Christian Barrientos
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (300.511 KB) | DOI: 10.19184/ijc.2020.4.1.5

Abstract

In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with n edges and at most n vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all n-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle C3 in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle C4t to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.
On b-edge consecutive edge labeling of some regular tree Kiki Ariyanti Sugeng; Denny R. Silaban
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.1.7

Abstract

Let G = (V, E) be a finite (non-empty), simple, connected and undirected graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from V ∪ E to the integers 1, 2, . . . , n + e, with the property that for every xy ∈ E, α(x) + α(y) + α(xy) = k, for some constant k. Such a labeling is called a b-edge consecutive edge magic total if α(E) = {b + 1, b + 2, . . . , b + e}. In this paper, we proved that several classes of regular trees, such as regular caterpillars, regular firecrackers, regular caterpillar-like trees, regular path-like trees, and regular banana trees, have a b-edge consecutive edge magic labeling for some 0 < b < |V |.
On M-unambiguity of Parikh matrices Wen Chean Teh
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (238.38 KB) | DOI: 10.19184/ijc.2020.4.1.1

Abstract

The Parikh matrix mapping was introduced by Mateescu et al. in 2001 as a canonical generalization of the classical Parikh mapping. The injectivity problem of Parikh matrices, even for ternary case, has withstanded numerous attempts over a decade by various researchers, among whom is Serbanuta. Certain M-ambiguous words are crucial in Serbanuta's findings about the number of M-unambiguous prints. We will show that these words are in fact strongly M-ambiguous, thus suggesting a possible extension of Serbanuta’s work to the context of strong M-equivalence. In addition, initial results pertaining to a related conjecture by Serbanuta will be presented.
Computing total edge irregularity strength of some n-uniform cactus chain graphs and related chain graphs Isnaini Rosyida; Diari Indriati
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.1.6

Abstract

Given graph G(V,E). We use the notion of total k-labeling which is edge irregular. The notion of total edge irregularity strength (tes) of graph G means the minimum integer k used in the edge irregular total k-labeling of G. A cactus graph G is a connected graph where no edge lies in more than one cycle. A cactus graph consisting of some blocks where each block is cycle Cn with same size n is named an n-uniform cactus graph. If each cycle of the cactus graph has no more than two cut-vertices and each cut-vertex is shared by exactly two cycles, then G is called n-uniform cactus chain graph. In this paper, we determine tes of n-uniform cactus chain graphs C(Cnr) of length r for some n ≡ 0 mod 3. We also investigate tes of related chain graphs, i.e. tadpole chain graphs Tr(4,n) and Tr(5,n) of length r. Our results are as follows: tes(C(Cnr)) = ⌈(nr + 2)/3⌉ ; tes(Tr(4,n)) = ⌈((5+n)r+2)/3⌉ ; tes(Tr(5,n)) = ⌈((5+n)r+2)/3⌉.
A Note on Edge Irregularity Strength of Some Graphs I Nengah Suparta; I Gusti Putu Suharta
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (524.395 KB) | DOI: 10.19184/ijc.2020.4.1.2

Abstract

Let G(V, E) be a finite simple graph and k be some positive integer. A vertex k-labeling of graph G(V,E), Φ : V → {1,2,..., k}, is called edge irregular k-labeling if the edge weights of any two different edges in G are distinct, where the edge weight of e = xy ∈ E(G), wΦ(e), is defined as wΦ(e) = Φ(x) + Φ(y). The edge irregularity strength for graph G is the minimum value of k such that Φ is irregular edge k-labeling for G. In this note we derive the edge irregularity strength of chain graphs mK3−path for m ≢ 3 (mod4) and C[Cn(m)] for all positive integers n ≡ 0 (mod 4) 3n and m. We also propose bounds for the edge irregularity strength of join graph Pm + Ǩn for all integers m, n ≥ 3.
Randomness of encryption keys generated by super H-antimagic total labeling Antonius Cahya Prihandoko; Yudha Alif Auliya; Diksy Media Firmansyah; S Slamin
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.1.3

Abstract

SuperH-antimagic total labeling (SHATL) can be utilized to generate encryption keys. The keys are then used to establish the improved block and stream ciphers. In these ciphers, different blocks were encrypted by the different keys, but all block keys were connected one another. These conditions make the developed cryptosystems more secure and require less keys storage capacity compared to the ordinary block and stream cipher. The randomness of the generated keys, however, still need to be tested. The test is necessary to ensure that there is no specific pattern that can be utilized by any intruder to guess the keys. This paper presents the randomness tests applied to all key sequences generated by both the improved block scheme and the stream based scheme.
On locating-dominating number of comb product graphs Aswan Anggun Pribadi; Suhadi Wido Saputro
Indonesian Journal of Combinatorics Vol 4, No 1 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (171.715 KB) | DOI: 10.19184/ijc.2020.4.1.4

Abstract

We consider a set D ⊆ V(G) which dominate G and for every two distinct vertices x, y ∈ V(G) \ D, the open neighborhood of x and y in D are different. The minimum cardinality of D is called the locating-dominating number of G. In this paper, we determine an exact value of the locating- dominating number of comb product graphs of any two connected graphs of order at least two.

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