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Coherent configurations over copies of association schemes of prime order
Sharafdini, Reza,Hirasaka, Mitsugu University of Primorska Press 2017 Ars mathematica contemporanea Vol.12 No.1
<P>In this paper we consider a combinatorial analogue to this fact through the theory of coherent configurations, and give some arithmetic sufficient conditions for a coherent configuration with two homogeneous components of prime order to be uniquely determined by one of the homogeneous components.</P>
On Diameter, Cyclomatic Number and Inverse Degree of Chemical Graphs
Reza Sharafdini,Ali Ghalavand,Ali Reza Ashrafi 경북대학교 자연과학대학 수학과 2020 Kyungpook mathematical journal Vol.60 No.3
Let G be a chemical graph with vertex set {v1, v1, . . . , vn} and degree sequence d(G) = (degG(v1), degG(v2), . . . , degG(vn)). The inverse degree, R(G) of G is defined as R(G) = Pni=11degG(vi). The cyclomatic number of G is defined as γ = m − n + k, where m, n and k are the number of edges, vertices and components of G, respectively. In this paper, some upper bounds on the diameter of a chemical graph in terms of its inverse degree are given. We also obtain an ordering of connected chemical graphs with respect to the inverse degree.
Characterization of balanced coherent configurations
Hirasaka, Mitsugu,Sharafdini, Reza Elsevier 2010 Journal of algebra Vol.324 No.8
<P><B>Abstract</B></P><P>Let <I>G</I> be a group acting on a finite set <I>Ω</I>. Then <I>G</I> acts on Ω×Ω by its entry-wise action and its orbits form the basis relations of a coherent configuration (or shortly scheme). Our concern is to consider what follows from the assumption that the number of orbits of <I>G</I> on <SUB>Ωi</SUB>×<SUB>Ωj</SUB> is constant whenever <SUB>Ωi</SUB> and <SUB>Ωj</SUB> are orbits of <I>G</I> on <I>Ω</I>. One can conclude from the assumption that the actions of <I>G</I> on <SUB>Ωi</SUB>'s have the same permutation character and are not necessarily equivalent. From this viewpoint one may ask how many inequivalent actions of a given group with the same permutation character there exist. In this article we will approach to this question by a purely combinatorial method in terms of schemes and investigate the following topics: (i) balanced schemes and their central primitive idempotents, (ii) characterization of reduced balanced schemes.</P>
EXTREMAL CHEMICAL TREES WITH RESPECT TO HYPER-ZAGREB INDEX
Ali Ghalavand,Ali Reza Ashrafi,Reza Sharafdini,Ottorino Ori 한국수학교육학회 2019 純粹 및 應用數學 Vol.26 No.3
Suppose G is a molecular graph with edge set E(G). The Hyper-Zagreb index of G is defined as $ HM(G)=sum_{uv\in E(G)}[deg_{G}(u) + deg_{G}(v)]^2$, where $deg_G(u)$ is the degree of a vertex u in G. In this paper, we characterize the chemical trees of order $n=> 12$ with the first twenty smallest Hyper-Zagreb index are characterized.