# Journal of Discrete Mathematics and Its Applications Volume:8 Issue: 2, Spring 2023

• تاریخ انتشار: 1402/04/10
• تعداد عناوین: 6
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• Najaf Amraei * Pages 49-63
The symmetric division degree (SDD) index is one the 148 discrete Adriatic indices,introduced by Vukicevi´c et al. as a remarkable predictor of total surface area of polychlorobiphenyls.The SDD index has already been proved a valuable index in the QSPR/QSAR studies. This paper isessentially a survey of known results about bounds for SDD index of graphs.
Keywords: symmetric division degree index, extremal graphs, vertex-degree-based index
• Stefan Stankov, Marjan Matejic, Igor Milovanovic *, Emina Milovanovic Pages 65-74
Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$.Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots \ge d(e_m)=\delta_e$, sequences of vertex and edge degrees, respectively. The first reformulated Zagreb index (coindex) is defined as $\displaystyle EM_1(G)=\sum_{i=1}^m d(e_i)^2 = \sum_{e_i\sim e_j}(d(e_i)+d(e_j))$ $\Big(\displaystyle \overline{EM}_1(G) = \sum_{e_i\nsim e_j}(d(e_i)+d(e_j))\Big)$.We consider relationship between reformulated Zagreb indices/coindices and determine their bounds in terms of some basic graph parameters.
Keywords: Topological indices, Zagreb indices, Line graph
• P .Chella Pandian Pages 75-82

In this paper, lower bound and upper bound on the covering radius ofDNA codes over a finite ring N with respect to Chinese euclidean distanceare given. Also determine the covering radius of various Repetition DNAcodes, Simplex DNA code Type α and Simplex DNA code Type β andbounds on the covering radius for MacDonald DNA codes of both typesover N.

Keywords: DNA Code, Finite Ring, Covering Radius, Simplex Codes
• Razie Alidehi Ravandi *, Herish Omer Abdullah Pages 83-103
This paper presents a comprehensive analysis of the role of topological indices and centrality measures in predicting the chemical properties of molecules, with a specific focus on six drugs known for their effectiveness in treating corona. The molecular structures of these drugs were carefully examined, and a range of topological indices were calculated. Utilizing regression analysis techniques, we reveal significant relationships between the chemical parameters of the drugs and two specific indices, namely ISI5 and ISI6, as well as various centrality measures.
Keywords: Topological indices, chemical properties, centrality measures
• Saeed Mohammadian Semnani *, Samira Sabeti Pages 105-112
Given a graph G with vertex set V (G) = {v1, v2, · · · , vn}. Let di be the degree of the vertex vi in G for i = 1,2, · · ·, n. We introduce the sum of degrees and the product of degrees matrices of a graph. Furthermore, we consider the central indices matrix as an Arithmetic mean matrix, Geometric mean matrix, and Harmonic mean matrix. The spectral of these matrices has been computed. In this paper, we investigate the central indices energy of some classes of graphs and several results concerning its energy have been obtained.
Keywords: eigenvalue of a graph, energy, geometric mean energy, arithmetic mean energy, harmonic mean energy
• Modjtaba Ghorbani, Aziz Seyyedhadi, Farzaneh Nowroozi-Larki Pages 113-123

A graph is called one-regular if its full automorphism group acts regularly on the set of arcs. In this paper, we classify all connected one-regular graphs of valency 4 of order $p^2q^2$, where $p>q$ are prime numbers. We also prove that all such graphs are Cayley graphs.

Keywords: one-regular graph, symmetric graph, Cayley graph