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All Journal Indonesian Journal of Combinatorics
Jona Martinus Manulang
Universitas Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management

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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)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (215.735 KB) | DOI: 10.19184/ijc.2018.2.1.2

Abstract

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.
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)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (332.422 KB) | 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.
Co-Authors Dina Eka Nurvazly Kiki A. Sugeng