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All Journal Indonesian Journal of Combinatorics
Haval Mohammed Salih
Soran University
Computer Science & IT Decision Sciences, Operations Research & Management

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Prime ideal graphs of commutative rings Haval Mohammed Salih; Asaad A. Jund
Indonesian Journal of Combinatorics Vol 6, No 1 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.1.2

Abstract

Let R be a finite commutative ring with identity and P be a prime ideal of R. The vertex set is R - {0} and two distinct vertices are adjacent if their product in P. This graph is called the prime ideal graph of R and denoted by ΓP. The relationship among prime ideal, zero-divisor, nilpotent and unit graphs are studied. Also, we show that ΓP is simple connected graph with diameter less than or equal to two and both the clique number and the chromatic number of the graph are equal. Furthermore, it has girth 3 if it contains a cycle. In addition, we compute the number of edges of this graph and investigate some properties of ΓP.
Index graphs of finite permutation groups Haval Mohammed Salih
Indonesian Journal of Combinatorics Vol 6, No 2 (2022)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2022.6.2.2

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.
On graphs associated to topological spaces Haval Mohammed Salih
Indonesian Journal of Combinatorics Vol 7, No 1 (2023)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2023.7.1.5

Abstract

Let ???? be a set and (????,????) be a topological space. A new type of graph on ????(????), namely the closure graph of ???? is introduced. The closure graph denoted by Γc whose vertex set is ????(????) in which two distinct vertices ???? and ???? are adjacent if A'∩B' ⊆ (A∩B)'. In this paper, the closure graph is shown as a simple, connected graph with diameter at most two. Furthermore, the girth of the closure graph Γcof ???? is three if ???? contains more than one point. Also, several graph properties are studied.
Co-Authors Asaad A. Jund