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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 6 Documents

Search results for , issue "Vol 3, No 2 (2019)" : 6 Documents clear

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.

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.

On size multipartite Ramsey numbers for stars Anie Lusiani; Edy Tri Baskoro; Suhadi Wido Saputro
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Burger and Vuuren defined the size multipartite Ramsey number for a pair of complete, balanced, multipartite graphs mj(Kaxb,Kcxd), for natural numbers a,b,c,d and j, where a,c >= 2, in 2004. They have also determined the necessary and sufficient conditions for the existence of size multipartite Ramsey numbers mj(Kaxb,Kcxd). Syafrizal et al. generalized this definition by removing the completeness requirement. For simple graphs G and H, they defined the size multipartite Ramsey number mj(G,H) as the smallest natural number t such that any red-blue coloring on the edges of Kjxt contains a red G or a blue H as a subgraph. In this paper, we determine the necessary and sufficient conditions for the existence of multipartite Ramsey numbers mj(G,H), where both G and H are non complete graphs. Furthermore, we determine the exact values of the size multipartite Ramsey numbers mj(K1,m, K1,n) for all integers m,n >= 1 and j = 2,3, where K1,m is a star of order m+1. In addition, we also determine the lower bound of m3(kK1,m, C3), where kK1,m is a disjoint union of k copies of a star K1,m and C3 is a cycle of order 3.

The locating-chromatic number and partition dimension of fibonacene graphs Ratih Suryaningsih; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Fibonacenes are unbranched catacondensed benzenoid hydrocarbons in which all the non-terminal hexagons are angularly annelated. A hexagon is said to be angularly annelated if the hexagon is adjacent to exactly two other hexagons and possesses two adjacent vertices of degree 2. Fibonacenes possess remarkable properties related with Fibonacci numbers. Various graph properties of fibonacenes have been extensively studied, such as their saturation numbers, independence numbers and Wiener indices. In this paper, we show that the locating-chromatic number of any fibonacene graph is 4 and the partition dimension of such a graph is 3.

Super local edge anti-magic total coloring of paths and its derivation Fawwaz Fakhrurrozi Hadiputra; Denny Riama Silaban; Tita Khalis Maryati
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Suppose G(V,E) be a connected simple graph and suppose u,v,x be vertices of graph G. A bijection f : V ∪ E → {1,2,3,...,|V (G)| + |E(G)|} is called super local edge antimagic total labeling if for any adjacent edges uv and vx, w(uv) 6= w(vx), which w(uv) = f(u)+f(uv)+f(v) for every vertex u,v,x in G, and f(u) < f(e) for every vertex u and edge e ∈ E(G). Let γ(G) is the chromatic number of edge coloring of a graph G. By giving G a labeling of f, we denotes the minimum weight of edges needed in G as γleat(G). If every labels for vertices is smaller than its edges, then it is be considered γsleat(G). In this study, we proved the γ sleat of paths and its derivation.

On the total vertex irregularity strength of comb product of two cycles and two stars Rismawati Ramdani
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G = (V(G),E(G)) be a graph and k be a positive integer. A total k-labeling of G is a map f : V ∪ E → {1,2,3,...,k}. The vertex weight v under the labeling f is denoted by w_f(v) and defined by w_f(v) = f(v) + \sum_{uv \in{E(G)}} {f(uv)}. A total k-labeling of G is called vertex irregular if there are no two vertices with the same weight. The total vertex irregularity strength of G, denoted by tvs(G), is the minimum k such that G has a vertex irregular total k-labeling. This labelings were introduced by Baca, Jendrol, Miller, and Ryan in 2007. Let G and H be two connected graphs. Let o be a vertex of H. The comb product between G and H, denoted by G \rhd_o H, is a graph obtained by taking one copy of G and |V(G)| copies of H and grafting the i-th copy of H at the vertex o to the i-th vertex of G. In this paper, we determine the total vertex irregularity strength of comb product of two cycles and two stars.

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