Publisher: Indonesian Combinatorial Society (InaCombS)   (Total: 1 journals)   [Sort by number of followers]

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Indonesian J. of Combinatorics     Open Access  
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Indonesian Journal of Combinatorics
Number of Followers: 0  

  This is an Open Access Journal Open Access journal
ISSN (Online) 2541-2205
Published by Indonesian Combinatorial Society (InaCombS) Homepage  [1 journal]
  • On the number of caterpillars

    • Authors: Christian Barrientos
      Pages: 77 - 96
      Abstract: A caterpillar is a tree obtained from a path by attaching pendant vertices. The number of caterpillars of size n is a well-known result. In this work extend this result exploring the number of caterpillars of size n together with the cardinalities of the stable sets and the diameter. Three closed formulas are presented, giving the number of caterpillars of size n with: (i) smaller stable set of cardinality k, (ii) diameter d, and (iii) diameter d and smaller stable set of cardinality k.
      PubDate: 2022-12-31
      DOI: 10.19184/ijc.2022.6.2.1
      Issue No: Vol. 6, No. 2 (2022)
  • Index graphs of finite permutation groups

    • Authors: haval Mohammed Salih
      Pages: 97 - 104
      Abstract: Let G be a subgroup of Sn. For x ∈ G, the index of x in G is denoted by ind x is the minimal number of 2-cycles needed to express x as a product. In this paper, we define a new kind of graph on G, namely the index graph and denoted by Γind(G). Its vertex set the set of all conjugacy classes of G and two distinct vertices x ∈ Cx and y ∈ Cy are adjacent if Gcd(ind x, ind y) 6 ≠ 1. We study some properties of this graph for the symmetric groups Sn, the alternating group An, the cyclic group Cn, the dihedral group D2n and the generalized quaternain group Q4n. In particular, we are interested in the connectedness of them.
      PubDate: 2022-12-31
      DOI: 10.19184/ijc.2022.6.2.2
      Issue No: Vol. 6, No. 2 (2022)
  • The total vertex irregularity strength of symmetric cubic graphs of the
           Foster's Census

    • Authors: Rika Yanti, Gregory Benedict Tanidi, Suhadi Wido Saputro, Edy Tri Baskoro
      Pages: 105 - 119
      Abstract: Foster (1932) performed a mathematical census for all connected symmetric cubic (trivalent) graphs of order n with n ≤ 512. This census then was continued by Conder et al. (2006) and they obtained the complete list of all connected symmetric cubic graphs with order n ≤ 768. In this paper, we determine the total vertex irregularity strength of such graphs obtained by Foster. As a result, all the values of the total vertex irregularity strengths of the symmetric cubic graphs of order n from Foster census strengthen the conjecture stated by Nurdin, Baskoro, Gaos & Salman (2010), namely ⌈(n+3)/4⌉.
      PubDate: 2022-12-31
      DOI: 10.19184/ijc.2022.6.2.3
      Issue No: Vol. 6, No. 2 (2022)
  • Hamming index of graphs with respect to its incidence matrix

    • Authors: Harishchandra S. Ramane, Ishwar B. Baidari, Raju B. Jummannaver, Vinayak V. Manjalapur, Gouramma A. Gudodagi, Ashwini S. Yalnaik, Ajith S. Hanagawadimath
      Pages: 120 - 129
      Abstract: Let $B(G)$ be the incidence matrix of a graph $G$. The row in $B(G)$ corresponding to a vertex $v$, denoted by $s(v)$ is the string which belongs to $\Bbb{Z}_2^n$, a set of $n$-tuples over a field of order two. The Hamming distance between the strings $s(u)$ and $s(v)$ is the number of positions in which $s(u)$ and $s(v)$ differ. In this paper we obtain the Hamming distance between the strings generated by the incidence matrix of a graph. The sum of Hamming distances between all pairs of strings, called Hamming index of a graph is obtained.
      PubDate: 2022-12-31
      DOI: 10.19184/ijc.2022.6.2.4
      Issue No: Vol. 6, No. 2 (2022)
  • On generalized composed properties of generalized product graphs

    • Authors: Nopparat Pleanmani, Sayan Panma
      Pages: 130 - 142
      Abstract: A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class of all finite simple graphs. A nonempty set S of vertices of a graph G is said to be a ℘-set of G if G[S]∈ ℘. The maximum and minimum cardinalities of a ℘-set of G are denoted by M℘(G) and m℘(G), respectively. If S is a ℘-set such that its cardinality equals M℘(G) or m℘(G), we say that S is an M℘-set or an m℘-set of G, respectively. In this paper, we not only define six types of property ℘ by the using concepts of graph product and generalized graph product, but we also obtain M℘ and m℘ of product graphs in each type and characterize its M℘-set.
      PubDate: 2022-12-31
      DOI: 10.19184/ijc.2022.6.2.5
      Issue No: Vol. 6, No. 2 (2022)
School of Mathematical and Computer Sciences
Heriot-Watt University
Edinburgh, EH14 4AS, UK
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