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INDONESIA
Indonesian Journal of Combinatorics
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).
Arjuna Subject : -
Articles 5 Documents
 1 
Search results for , issue "Vol 1, No 2 (2017)" : 5 Documents clear
Zagreb indices of block-edge transformation graphs and their complements Bommanahal Basavanagoud; Shreekant Patil
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (467.988 KB) | DOI: 10.19184/ijc.2017.1.2.3

Abstract

In this paper, we obtain expressions for first and second Zagreb indices and coindices of block-edge transformation graphs G^{ab}. Analogous expressions are obtained also for the complements of G^{ab}.
A strict upper bound for size multipartite Ramsey numbers of paths versus stars Chula Jayawardene; Lilanthi Samarasekara
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (188.112 KB) | DOI: 10.19184/ijc.2017.1.2.2

Abstract

Let $P_n$ represent the path of size $n$. Let $K_{1,m-1}$ represent a star of size $m$ and be denoted by $S_{m}$. Given a two coloring of the edges of a complete graph $K_{j \times s}$ we say that $K_{j \times s}\rightarrow (P_n,S_{m+1})$ if there is a copy of $P_n$ in the first color or a copy of $S_{m+1}$ in the second color. The size Ramsey multipartite number $m_j(P_n, S_{m+1})$ is the smallest natural number $s$ such that $K_{j \times s}\rightarrow (P_n,S_{m+1})$. Given $j,n,m$ if $s=\left\lceil \dfrac{n+m-1-k}{j-1} \right\rceil$, in this paper, we show that the size Ramsey numbers $m_j(P_n,S_{m+1})$ is bounded above by $s$ for $k=\left\lceil \dfrac{n-1}{j} \right\rceil$. Given $j\ge 3$ and $s$, we will obtain an infinite class $(n,m)$ that achieves this upper bound $s$. In the later part of the paper, will also investigate necessary and sufficient conditions needed for the upper bound to hold.
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)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (130.031 KB) | DOI: 10.19184/ijc.2017.1.2.4

Abstract

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.
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)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (183.847 KB) | DOI: 10.19184/ijc.2017.1.2.5

Abstract

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.
Some results on cordiality labeling of generalized Jahangir graph Roslan Hasni; S. Matarneh; Almothana Azaizeh
Indonesian Journal of Combinatorics Vol 1, No 2 (2017)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (230.072 KB) | DOI: 10.19184/ijc.2017.1.2.1

Abstract

In this paper we consider the cordiality of a generalized Jahangir graph $J_{n,m}$. We give sufficient condition for $J_{n,m}$ to admit (or not admit) the prime cordial labeling, product cordial labeling and total product cordial labeling.

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