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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 7 Documents

Search results for , issue "Vol 2, No 2 (2018)" : 7 Documents clear

Another H-super magic decompositions of the lexicographic product of graphs H Hendy; Kiki A. Sugeng; A.N.M Salman; Nisa Ayunda
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let H and G be two simple graphs. The concept of an H-magic decomposition of G arises from the combination between graph decomposition and graph labeling. A decomposition of a graph G into isomorphic copies of a graph H is H-magic if there is a bijection f : V(G) ∪ E(G) → {1, 2, ..., ∣V(G) ∪ E(G)∣} such that the sum of labels of edges and vertices of each copy of H in the decomposition is constant. A lexicographic product of two graphs G1 and G2, denoted by G1[G2], is a graph which arises from G1 by replacing each vertex of G1 by a copy of the G2 and each edge of G1 by all edges of the complete bipartite graph Kn, n where n is the order of G2. In this paper we provide a sufficient condition for $\overline{C_{n}}[\overline{K_{m}}]$ in order to have a $P_{t}[\overline{K_{m}}]$-magic decompositions, where n > 3, m > 1, and t = 3, 4, n − 2.

On star coloring of Mycielskians K. Kaliraj; V. Kowsalya; Vernold Vivin
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

In a search for triangle-free graphs with arbitrarily large chromatic numbers, Mycielski developed a graph transformation that transforms a graph G into a new graph μ(G), we now call the Mycielskian of G, which has the same clique number as G and whose chromatic number equals χ(G) + 1. In this paper, we find the star chromatic number for the Mycielskian graph of complete graphs, paths, cycles and complete bipartite graphs.

On the local metric dimension of t-fold wheel, Pn o Km, and generalized fan Rokhana Ayu Solekhah; Tri Atmojo Kusmayadi
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G be a connected graph and let u, v ∈ V(G). For an ordered set W = {w1, w2, ..., wn} of n distinct vertices in G, the representation of a vertex v of G with respect to W is the n-vector r(v∣W) = (d(v, w1), d(v, w2), ..., d(v, wn)), where d(v, wi) is the distance between v and wi for 1 ≤ i ≤ n. The set W is a local metric set of G if r(u ∣ W) ≠ r(v ∣ W) for every pair u, v of adjacent vertices of G. The local metric set of G with minimum cardinality is called a local metric basis for G and its cardinality is called a local metric dimension, denoted by lmd(G). In this paper we determine the local metric dimension of a t-fold wheel graph, Pn ⊙ Km graph, and generalized fan graph.

Application of generalised hierarchical product of graphs for computing F-index of four operations on graphs Nilanjan De
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph which was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced. In this paper we study the F-index of four operations on graphs which were introduced by Eliasi and Taeri, and hence using the derived results we find F-index of some particular and chemically interesting graphs.

Edge magic total labeling of lexicographic product C4(2r+1) o ~K2 cycle with chords, unions of paths, and unions of cycles and paths Inne Singgih
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

An edge magic total (EMT) labeling of a graph G = (V, E) is a bijection from the set of vertices and edges to a set of numbers defined by λ : V ∪ E → {1, 2, ..., ∣V∣ + ∣E∣} with the property that for every xy ∈ E, the weight of xy equals to a constant k, that is, λ(x) + λ(y) + λ(xy) = k for some integer k. In this paper given the construction of an EMT labeling for certain lexicographic product $C_{4(2r+1)}\circ \overline{K_2}$, cycle with chords [c]tCn, unions of paths mPn, and unions of cycles and paths m(Cn1(2r + 1) ∪ (2r + 1)Pn2).

Z2nm-supermagic labeling of Cn#Cm Dalibor Froncek; James McKeown; John McKeown; Michael McKeown
Indonesian Journal of Combinatorics Vol 2, No 2 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

A Γ-supermagic labeling of a graph G = (V, E) with ∣E∣ = k is a bijection from E to an Abelian group Γ of order k such that the sum of labels of all incident edges of every vertex x ∈ V is equal to the same element μ ∈ Γ. We present a Z2nm-supermagic labeling of Cartesian product of two cycles, Cn□Cm for n odd. This along with an earlier result by Ivančo proves that a Z2nm-supermagic labeling of Cn□Cm exists for every n, m ≥ 3.

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.

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Slamin

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