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All Journal Indonesian Journal of Combinatorics

Kiki A. Sugeng

Universitas Indonesia

Author-ID : 3670770

Computer Science & IT Decision Sciences, Operations Research & Management

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Articles

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.

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.

Rainbow connection number of Cm o Pn and Cm o Cn Alfi Maulani; Soya Pradini; Dian Setyorini; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G = (V(G),E(G)) be a nontrivial connected graph. A rainbow path is a path which is each edge colored with different color. A rainbow coloring is a coloring which any two vertices should be joined by at least one rainbow path. For two different vertices, u,v in G, a geodesic path of u-v is the shortest rainbow path of u-v. A strong rainbow coloring is a coloring which any two vertices joined by at least one rainbow geodesic. A rainbow connection number of a graph, denoted by rc(G), is the smallest number of color required for graph G to be said as rainbow connected. The strong rainbow color number, denoted by src(G), is the least number of color which is needed to color every geodesic path in the graph G to be rainbow. In this paper, we will determine the rainbow connection and strong rainbow connection for Corona Graph Cm o Pn, and Cm o Cn.

Orthogonal labeling Bernard Immanuel; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let ∆G be the maximum degree of a simple connected graph G(V,E). An injective mapping P : V → R∆G is said to be an orthogonal labeling of G if uv,uw ∈ E implying (P(v) − P(u)) · (P(w) − P(u)) = 0, where · is the usual dot product defined in Euclidean space. A graph G which has an orthogonal labeling is called an orthogonal graph. This labeling is motivated by the existence of several labelings defined by some algebraic structure, i.e. harmonious labeling and group distance magic labeling. In this paper we study some preliminary results on orthogonal labeling. One of the early result is the fact that cycle graph with even vertices are orthogonal, while ones with odd vertices are not. The main results in this paper state that any graph containing K3 as its subgraph is non-orthogonal and that a graph G′ obtained from adding a pendant to a vertex in orthogonal graph G is orthogonal. In the end of the paper we state the corollary that any tree is orthogonal.

Relationship between adjacency and distance matrix of graph of diameter two Siti L. Chasanah; Elvi Khairunnisa; Muhammad Yusuf; Kiki A. Sugeng
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.1

The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0. In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is D=2(J-I)-A. From this relationship, we also determine the value of the determinant matrix A+D and the upper bound of determinant of matrix D.

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.

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

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.

Co-Authors A.N.M Salman Alfi Maulani Bernard Immanuel Dian Setyorini Dina Eka Nurvazly Elvi Khairunnisa H Hendy Jona Martinus Manulang Khairunnisa N. Afifah MUHAMMAD YUSUF Nisa Ayunda Siti L. Chasanah Soya Pradini

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