Search

This paper focuses on the power graph of dihedral groups of order 2n, D2n, where n ≥ 3. We show the characteristic polynomial of the power graph corresponding to the adjacency, Laplacian, signless Laplacian, and normalized form of these matrices. [ABSTRACT FROM AUTHOR]

This paper focuses on the non-commuting graph for dihedral groups of order 2n, D2n, where n ≥ 3. We show the spectrum and energy of the graph corresponding to the closeness matrix. The result is that the obtained energy is always twice its spectral radius and is never an odd integer. Moreover, it is classified as hypoenergetic. [ABSTRACT FROM AUTHOR]

A Q-neutrosophic soft environment is an innovative hybrid tool that combines features of both a Q-neutrosophic set (Q-NS) and a parametric tool "soft set" (SS) in order to manage imprecise and indeterminate situations in various mathematical problems. In this article, we introduce a new algebraic approach called Q-neutrosophic soft matrices (Q-NSMs) to address the issues of two-dimensional (two variables) in a universal set by representing the concept of Q-neutrosophic soft sets (Q-NSSs) in matrices. On Q-NSMs, we define the fundamental set operations and some algebraic operations, i.e., complement, union, intersection, addition, subtraction, multiplication, and scalar multiplication, and prove related properties of these operations. Moreover, these operations are illustrated via several numerical examples. Then, two algorithms are proposed to tackle group decision making (GDM) problems: The first depends on the score function of Q-NSMs, and the second is based on the aggregation operator of Q-NSMs. Finally, this study is supported by a brief comparison with some relevant previous models. [ABSTRACT FROM AUTHOR]

Let ΓG and ΓG be the commuting and non-commuting graphs on a finite group G, respectively, having G\Z(G) as the vertex set, where Z(G) is the center of G. The order of ΓG and ΓG is ΙG\Z(G)Ι, denoted by m. For ΓG, the edge joining two distinct vertices vp, vq ∈ G\Z(G) if and only if vpvq ≠= vqvp, on the other hand, whenever they commute in G, vp and vq are adjacent in ΓG. The degree subtraction matrix (DSt) of ΓG is denoted by DSt(ΓG), so that its (p, q)-entry is equal to dvp - dvq, if vp ≠ = vq, and zero if vp = vq, where dvp is the degree of vp. For i = 1, 2, ..., m, the maximum of ΙλiΙ as the DSt-spectral radius of ΓG and the sum of ΙλiΙ as DSt-energy of ΓG, where λi are the eigenvalues of DSt(ΓG). These notations can be applied analogously to the degree subtraction matrix of the commuting graph, DSt(ΓG). Throughout this paper, we provide DSt-spectral radius and DSt-energy of ΓG and ΓG for dihedral groups of order 2n, where n ≥ 3. We then present the correlation of the energies and their spectral radius. [ABSTRACT FROM AUTHOR]