Journal of Discrete Mathematics and Its Applications
https://jdma.sru.ac.ir/
Journal of Discrete Mathematics and Its Applicationsendaily1Sun, 01 Sep 2024 00:00:00 +0330Sun, 01 Sep 2024 00:00:00 +0330On the hierarchical product of graphs
https://jdma.sru.ac.ir/article_2173.html
The hierarchical product of graphs is a variant of the Cartesian product. It is associative, not commutative, and finite connected graphs have unique first prime factors with respect to it. We present examples of infinite graphs with different first prime factors, and show that homogeneous trees of finite degree have unique prime factoriza-tions with respect to the hierarchical product. On the way, we pose two problems.Automorphism group of a graph constructed from a lattice
https://jdma.sru.ac.ir/article_2183.html
Let $L$ be a lattice and $S$ be a $\wedge$-closed subset of $L$. The graph $\Gamma_{S}(L)$ is a simple graph with all elements of $L$ as vertex set and two distinct vertex $x,y$ are adjacent if and only if $x\vee y\in S$. In this paper, we verify the automorphism group of $\Gamma_{S}(L)$ and the relation by automorphism group of the lattice $L$. Also we study some properties of the graph $\Gamma_{S}(L)$ where $S$ is a prime filter or an ideal such as the perfect maching.Calculation of topological indices based on M-polynomial for polytrimethylene terephthalate
https://jdma.sru.ac.ir/article_2188.html
Polytrimethylene terephthalate is an extensively utilized thermoplastic industrial polymer characterized by a low melting point and minimal water absorption and it follows the general molecular formula $(C_{11}H_{10}O_{4}){n}$. It is interesting to chemists and engineering researchers due to its application in various industries, especially in textiles and engineering thermoplastics. In this article, the general formulas of some degree-based topological indices are obtained via M-polynomials for Polytrimethylene terephthalate. Calculating indices via these formulas does not require counting the degree of vertices or edge partitioning and can only be calculated by having the number of Polytrimethylene terephthalate monomers. The obtained results are displayed numerically and graphically, then the topological indices are graphically compared.Configuration sets; a right place for ping-pong arguments
https://jdma.sru.ac.ir/article_2187.html
Giving a condition for the amenability of groups, Rosenblatt and Willis first introducedthe concept of configuration. In this paper, we investigate the relationship between ping-pong lemma and configuration sets, and show that only one configuration set is enough to ensure that several elements in a group generates a free subgroup of that group. Using only one two-sided configuration sets, we give, in a sense, a generalization of this result to polycyclic or FC-groups. Finiteness and paradoxical decompositions of groups, are other properties which can be characterized with only one configuration set.On the Cayleyness of bipartite Kneser graphs
https://jdma.sru.ac.ir/article_2191.html
For any given $n,k \in \mathbb{N}$ with $ 2k &lt; n, $ the $bipartite\ Kneser \ graph$ $H(n, k)$ is defined as the graph whose vertex set is the family of $k$-subsets and ($n-k$)-subsets of $[n] = \{1, 2,\dots, n\}, $ in whichany two vertices are adjacent if and only if one of them is a subset of the other.In this paper, we study some algebraic properties of the bipartite Kneser graph $H(n, k)$. In particular, we determine the values of $n,k$, for which the bipartite Knesergraph $H(n,k)$ is a Cayley graph.A discussion of Feng-Liu operator and fixed point theorems on metric space
https://jdma.sru.ac.ir/article_2189.html
In this paper, a collection of various multi-valued fixed point results using Feng-Liu operator on metric space are examined. Comparative discussion on some of the important ideas, using this operators are presented. Thereafter the handful of potential improvements on the existing literature are proposed.Elliptic Sombor energy of a graph
https://jdma.sru.ac.ir/article_2184.html
Let $G$ be a simple graph with vertex set $V(G) = \{v_1, v_2,\ldots, v_n\}$. The elliptic Sombor matrix of $G$, denoted by $A_{ESO}(G)$, is defined as the $n\times n$ matrix whose $(i,j)$-entry is $(d_i+d_j)\sqrt{d_i^2+d_j^2}$ if $v_i$ and $v_j$ are adjacent and $0$ for another cases.Let the eigenvalues of the elliptic Sombor matrix $A_{ESO}(G)$ be $\rho_1\geq \rho_2\geq \ldots\geq \rho_n$ which are the roots of the elliptic Sombor characteristic polynomial $\prod_{i=1}^n (\rho-\rho_i)$. The elliptic Sombor energy ${E_{ESO}}$ of $G$ is the sum of absolute values of the eigenvalues of $A_{ESO}(G)$. In this paper, we compute the elliptic Sombor characteristic polynomial and the elliptic Sombor energy for some graph classes. We compute the elliptic Sombor energy of cubic graphs of order $10$ and as a consequence, we see that two $k$-regular graphs of the same order may have different elliptic Sombor energy.A review on perfect state transfer and pretty good state transfer of graphs
https://jdma.sru.ac.ir/article_2190.html
In this study, we review two significant topics: perfect State Transfer (PST) and Pretty Good State Transfer (PGST). These concepts involve designing interactions within a chain of spins on graph structures of networks, enabling a quantum state initially placed at one end to be perfectly or pretty transferred to the opposite end within a specified timeframe. PST and PGST play crucial roles in applications such as quantum information processing, quantum communication networks, and quantum chemistry