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In this study, a novel theoretical approach to describe thermo-optical elastic materials is proposed. This formulation offers insights into the relationship between plasma waves and thermomechanical waves when the microtemperature properties of semiconductor materials such as silicon are taken into account. The proposed model involves incorporating the concept of microtemperature effect according to photothermal (PT) excitation processes in nonlocal photo-thermoelasticity. The investigation of the electron-hole interaction concerning the elasto-thermodiffusion (ETD) theory in the context of thermoelastic (TD) and electronic (ED) deformation is the main focus of the work. The advanced model is utilized to analyze how the mechanical loading of ramp-like structures impacts the unrestricted nonlocality semiconductor material on a free outer plane. The Laplace transform approach in one-dimensional (1D) provides an analytical solution for main non-dimensional thermo-photo-elastic fields (the hole charge carrier field, the displacement (acoustic) wave, thermal wave, and plasma wave (carrier density). The primary fields in the Laplace domain are obtained analytically, and boundary conditions are established using a mechanical ramp type. Using a numerical inverse Laplace transform, full time domain solutions for the fundamental fields are obtained numerically according to the Riemann-sum approximation approach. The graphical representations illustrate and discuss the outcomes of the main physical fields. [ABSTRACT FROM AUTHOR]

Calculating and analyzing the number of spanning trees of networks (graphs) is an interesting and important research project in wide variety of fields, such as mathematics, theoretical computer science, chemistry, physics and so on. In this paper, we investigated the number of spanning trees in three sequences of families of graphs of the same average degree 14. We used the electrically equivalent transformations and rules of weighted generating function which avoids the laborious computation of the determinant for counting the number of spanning trees. Finally, we determined the entropy of our studied graphs. [ABSTRACT FROM AUTHOR]

The number of spanning trees is an important quantity characterizing the reliability of a network (graph). Generally, the number of spanning trees in a network can be obtained directly by calculating a related determinant corresponding to the network. However, for a large network, evaluating the relevant determinant is intractable. In this paper, we investigated the number of spanning trees in three sequences of families of graphs of the same average degree 16/3. We used the electrically equivalent transformations and rules of weighted generating function which avoids the laborious computation of the determinant for counting the number of spanning trees. Finally, we determined the entropy of our studied graphs. [ABSTRACT FROM AUTHOR]

The number of spanning trees is an important quantity characterizing the reliability of a network. In this paper, we find the explicit formulas of the number of spanning trees of some of the families of sequence graphs generated by triangle graph with its special feature in iteration. Using the electrically equivalent transformations, we obtain the weights of corresponding equivalent graphs and we further derive relationships for spanning trees between these graphs and transformed graphs. Finally, we compare the entropy of our graphs together and with other studied graphs of average degree. [ABSTRACT FROM AUTHOR]

Deriving closed formulae of the number of spanning trees for various graphs has attracted the attention of a lot of researchers. In this paper we derive simple and explicit formulas for the number of spanning trees in many classes of circulant graphs using the properties of Chebyshev polynomials. Deriving closed formulae of the number of spanning trees for various graphs has attracted the attention of a lot of researchers. In this paper we derive simple and explicit formulas for the number of spanning trees in many classes of circulant graphs using the properties of Chebyshev polynomials. [ABSTRACT FROM AUTHOR]

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this paper we derive simple formulas of the complexity, number of spanning trees of shadow of some graphs, using linear algebra, Chebyshev polynomials and matrix analysis techniques. [ABSTRACT FROM AUTHOR]

The number of spanning trees in graphs (networks) is an important invariant, it is also an important measure of reliability of a network. In this paper we derive simple formulas of the complexity, number of spanning trees, of some new graphs generated by a new operation, using linear algebra, Chebyshev polynomials and matrix analysis techniques. [ABSTRACT FROM AUTHOR]

In this paper we considered the set of regular CW-complexes or simply complexes. We obtained the necessary and sufficient condition for the composition of cellular maps to be a cellular folding. Also the necessary and sufficient condition for the composition of a cellular folding with a cellular map to be a cellular folding is declared. Then we proved that the Cartesian product of two cellular maps is a cellular folding is each map is a cellular folding. By using these results we proved some other results. Once again we generalized the first three results and in each case we obtained the folding graph of the new map in terms of the original ones. [ABSTRACT FROM AUTHOR]

Calculating the number of spanning trees of a graph is one of the widely studied graph problems since the Pioneer Gustav Kirchhoff (1847). In this work, using knowledge of difference equations we drive the explicit formulas for the number of spanning trees in the sequence of some Nonahedral (nine faced polyhedral) graphs generated by triangle using electrically equivalent transformations and rules of the weighted generating function. Finally, we evaluate the entropy of graphs in this manuscript with different studied graphs with an average degree being 4, 5 and 6., (© 2020 The Authors.)