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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 98 Documents

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New proofs of Konig's bipartite graph characterization theorem Salman Ghazal
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

We introduce four new elementary short proofs of the famous K\"{o}nig's theorem which characterizes bipartite graphs by absence of odd cycles. Our proofs are more elementary than earlier proofs because they use neither distances nor walks nor spanning trees.

Four new operations related to composition and their reformulated Zagreb index K Pattabiraman; A Santhakumar
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

The first reformulated Zagreb index EM1(G) of a simple graph G is defined as the sum of the terms (du + dv − 2)2 over all edges uv of G. In 2017, Sarala et al. introduced four new operations(F-product) of graphs. In this paper, we study the first reformulated Zagreb index for the F-product of some special well-known graphs such as subdivision and total 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.

Size multipartite Ramsey numbers for small paths versus books Chula J. Jayawardene; Jayampathy Ratnayake
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

Given $j \ge 2$, for graphs $G$ and $H$, the size Ramsey multipartite number $m_j(G, H)$ is defined as the smallest natural number $t$ such that any blue red coloring of the edges of the graph $K_{j \times t}$, necessarily containes a red $G$ or a blue $H$ as subgraphs. Let the book with $n$ pages is defined as the graph $K_1 + K_{1,n}$ and denoted by $B_n$. In this paper, we obtain the exact values of the size Ramsey numbers $m_j(P_3, H)$ for $j \ge 3$ where $H$ is a book $B_n$. We also derive some upper and lower bounds for the size Ramsey numbers $m_j(P_4, H)$ where $H$ is a book $B_n$.

Further results on edge irregularity strength of graphs Muhammad Imran; Adnan Aslam; Sohail Zafar; Waqas Nazeer
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

A vertex $k$-labelling $\phi:V(G)\longrightarrow \{1,2,\ldots,k\}$ is called irregular $k$-labeling of the graph $G$ if for every two different edges $e$ and $f$, there is $w_{\phi}(e)\neq w_{\phi}(f)$; where the weight of an edge is given by $e=xy\in E(G)$ is $w_{\phi (xy)=\phi(x)+\phi(y)$. The minimum $k$ for which the graph $G$ has an edge irregular $k$-labelling is called \emph{edge irregularity strength} of $G$, denoted by $es(G)$. In the paper, we determine the exact value of the edge irregularity strength of caterpillars, $n$-star graphs, $(n,t)$-kite graphs, cycle chains and friendship graphs.

Further Results on Locating Chromatic Number for Amalgamation of Stars Linking by One Path A. Asmiati; Lyra Yulianti; C. Ike Tri Widyastuti
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G = (V, E) be a connected graph. Let c be a proper coloring using k colors, namely 1, 2, ⋯, k. Let Π = {S1, S2, ⋯, Sk} be a partition of V(G) induced by c and let Si be the color class that receives the color i. The color code, cΠ(v) = (d(v, S1), d(v, S2), ⋯, d(v, Sk)), where d(v, Si) = min{d(v, x)∣x ∈ Si} for i ∈ [1, k]. If all vertices in V(G) have different color codes, then c is called as the locating-chromatic k-coloring of G. Minimum k such that G has the locating-chromatic k-coloring is called the locating-chromatic number, denoted by χL(G). In this paper, we discuss the locating-chromatic number for n certain amalgamation of stars linking a path, denoted by nSk, m, for n ≥ 1, m ≥ 2, k ≥ 3, and k > m.

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).

Dominating number of distance two of corona products of graphs Reni Umilasari; Darmaji Darmaji
Indonesian Journal of Combinatorics Vol 1, No 1 (2016)
Publisher : Indonesian Combinatorial Society (InaCombS)

Dominating set $S$ in graph $G=(V,E)$ is a subset of $V(G)$ such that every vertex of $G$ which is not element of $S$ are connected and have distance one to $S$. Minimum cardinality among dominating sets in a graph $G$ is called dominating number of graph $G$ and denoted by $\gamma(G)$. While dominating set ofdistance two which denoted by $S_2$ is a subset of $V(G)$ such that every vertex of $G$ which is not element of $S$ are connected and have maximum distance two to $S_2$. Dominating number of distance two $\gamma_2(G)$ is minimum cardinality of dominating set of distance two $S_2$. The corona $G \odot H$ of two graphs $G$ and $H$ where $G$ has $p$ vertices and $q$ edges is defined as the graph G obtained by taking one copy of $G$ and $p$ copies of $H$, and then joining by an edge the $i-th$ vertex of $G$ to every vertex in the $i-th$ copy of $H$. In this paper, we determine the dominating number of distance two of paths and cycles. We also determine the dominating number of distance two of corona product of path and any graphs as well as cycle and any graphs.

3-Difference cordial labeling of some path related graphs R Ponraj; M Maria Adaickalam; R Kala
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Let G be a (p, q)-graph. Let f : V(G) → {1, 2, …, k} be a map where k is an integer, 2 ≤ k ≤ p. For each edge uv, assign the label ∣f(u) − f(v)∣. f is called k-difference cordial labeling of G if ∣vf(i) − vf(j)∣ ≤ 1 and ∣ef(0) − ef(1)∣ ≤ 1 where vf(x) denotes the number of vertices labelled with x, ef(1) and ef(0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternate triangular snake, alternate quadrilateral snake, irregular triangular snake, irregular quadrilateral snake, double triangular snake, double quadrilateral snake, double alternate triangular snake, and double alternate quadrilateral snake.

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.

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