We characterize all graphs whose Laplacian energy equals that of their complement. A general spectral criterion is obtained and simplified for integer Laplacian spectra. These results yield several infinite families of complementarily Laplacian equienergetic graphs, including balanced unions of complete graphs, Cartesian products with $K_2$, and join-based constructions.
This paper presents a comprehensive computation of the character table of the group $SUT(2,q)$, defined as the group of $2 \times 2$ upper triangular matrices over the finite field $\mathbb{F}_{q}$ with determinant 1. For even $q$, we construct the character table using two distinct approaches. The first method employs the technique of coset analysis combined with Clifford-Fischer theory. The second method identifies $SUT(2,q)$ as a Frobenius group, whose representation theory is well-established, and derives its irreducible characters accordingly. For the case when $q$ is odd, the group is not a Frobenius group. Here, we determine the full set of irreducible characters through classical techniques, including lifting characters from the abelian quotient, and employing induction and restriction from related subgroups and the parent group $SL(2,q)$. In both cases, the complete character tables of $SUT(2,q)$ are explicitly computed and presented.
We introduce the notion of Z-semicommutative rings as a generalization of semicommutative rings. We find that the class of Z-semicommutative rings lies between the classes of central semicommutative rings and directly finite rings. We study some of its basic properties and characterizations with some extension rings. We show that a ring R is right Z-semicommutative if and only if xy = 0 =⇒ < x >< y >⊆ Zr(R) for every x, y ∈ R. Further, we show that the notions of clean rings and exchange rings are equivalent over the class of Z-semicommutative rings. Also, we discuss its connection with J-semicommutative rings.
This work presents a generalization of the Gardner equation withhigher-order dispersion and perturbation terms, replacing the beta derivativewith the Generalized Local Derivative (LGD). By introducing a kernelof weight N(β, t), the model captures the behavior of complex materialsand variable timescales that standard conformable operators cannot describe.Using the modified extended direct algebraic (mEDA) method,we transform the partial differential equation into an ordinary differentialequation to obtain exact soliton-like solutions.A comparative analysis is performed between three specific kernels: thebeta derivative, the Khalil conformable derivative, and the LGD with aMittag-Leffler kernel. The results demonstrate that the use of the Mittag-Leffler kernel introduces a non-local memory effect that alters the groupvelocity and the soliton trajectory. Finally, the linear stability analysisreveals that the LGD framework provides a more robust stability thresholdagainst high-frequency disturbances compared to rigid power models.
In this paper, we investigated the algebraic properties of a class of power associative RCC-loops (and its dual) and its relationship with some generalized forms of identities of first Bol-Moufang type (Cheban, Frute, Crazy) and second Bol-Moufang type of loops. Generalized forms of the left (right) alternative property and flexibility property were introduced and studied in this class of loops. We also explore the properties of the left representation set of this class of loops and constructed a loop of order $8$ belonging to this same class.
