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In 2011, Gross derived an O (n 2) -time algorithm to calculate the genus distribution of a given cubic Halin graph. In this paper, with the help of the overlap matrix, we obtain a recurrence relation for the Euler-genus polynomials of cubic caterpillar-Halin graphs. Explicit formulas for the embeddings of the cubic caterpillar-Halin graphs into surfaces with Euler-genus 0, 1 and 2 are also obtained. [ABSTRACT FROM AUTHOR]

For η ∈ { i , j , k } , a real quaternion matrix A is said to be η -Hermitian if A = A η ∗ , where A η ∗ = - η A ∗ η , and A ∗ stands for the conjugate transpose of A. In this paper, we present some practical necessary and sufficient conditions for the existence of an η -Hermitian solution to a system of constrained two-sided coupled real quaternion matrix equations and provide the general η -Hermitian solution to the system when it is solvable. Moreover, we present an algorithm and a numerical example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we use a result of N. S. Feldman to show that there are no supercyclic subnormal tuples in infinite dimensions. Also, we investigate some spectral properties of hypercyclic tuples of operators. Besides, we prove that if $$T$$ is a supercyclic $$\ell $$ -tuple of commuting $$n\times n$$ complex matrices, then $$\ell \ge n$$ and also there exists a supercyclic $$n$$ -tuple of commuting diagonal $$n\times n$$ matrices. Furthermore, we see that if $$T=(T_{1},\ldots ,T_{n})$$ is a supercyclic $$n$$ -tuple of commuting $$n\times n$$ complex matrices, then $$T_{j}$$ 's are simultaneously diagonalizable. [ABSTRACT FROM AUTHOR]