Özdemir de…ned the hybrid numbers as a generalization of complex, hyperbolic and dual numbers. In this research, we de…ne the generalized Lucas hybrinomials with two variables. Also, we get the Binet formula, generating function and some properties for the generalized Lucas hybrinomials. Moreover, Catalan's, Cassini's and d'Ocagne's identities for these hybrinomials are obtained. Lastly, by the help of the matrix theory we derive the matrix representation of the generalized Lucas hybrinomials.
In this paper, we first define the bi-periodic balancing quaternions. We give the generating function and Binet formula for this quaternion. Then, we obtain some identities and properties including this quaternion.
In this paper, we give some upper and lower bounds for the multiplicative Randic index, reduced reciprocal Randic index, Narumi-Katayama index and symmetric division index a graph using solely the vertex degrees. Then we obtain upper and lower bounds for these indices for the complete graphs, path graphs and Fibonacci-sum graphs. Finally, we compared the bounds of these indices for a general graph and some special graphs.
In this paper, we define the Horadam polynomials and hybrinomials with
two variables x and y; called the bivariate Horadam polynomials and
hybrinomials, respectively. Also, we obtain Binet formula, generating
function and some properties for the bivariate Horadam hybrinomials.
Moreover, we get Catalan, Cassini and d’Ocagne identities for these
hybrinomials. Finally, the matrix representations of the bivariate
Horadam hybrinomials were introduced.
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