**Volume 15** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Note on path signed graphs**

*Original research paper. Pages 1—6*

P. Siva Kota Reddy and M. S. Subramanya

Full paper (PDF, 129 Kb) | Abstract

*signed graphs*, graphs where every edge has a sign + or −, or

*marked graphs*, graphs where every vertex has a sign + or −. The

*path graph*P

_{k}(G) of a graph G is obtained by representing the paths P

_{k}in G by vertices whenever the corresponding paths P

_{k}in G form a path P

_{k+1}or a cycle C

_{k}. In this note, we introduce a natural extension of the notion of path graphs to the realm of signed graphs. It is shown that for any signed graph S, P

_{k}(S) is balanced. The concept of a line signed graph is generalized to that of a path signed graphs. Further, in this note we discuss the structural characterization of path signed graphs. Also, we characterize signed graphs which are switching equivalent to their path signed graphs P

_{3}(S) (P

_{4}(S)).

** On the linear systems over rhotrices**

*Original research paper. Pages 7—12*

Abdulhadi Aminu

Full paper (PDF, 147 Kb) | Abstract

*A*,

*B*and

*C*be rhotrices. In this paper we investigate systems of the form

*AB = C*and come up with conditions necessary for their solvability. We also outline a direct procedure for computing an

*n*-th root of a rhotrix.

**Structure and spectra of the components of primitive Pythagorean triples and Fermat’s last theorem**

*Original research paper. Pages 13—22*

J. V. Leyendekkers, A. G. Shannon and C. K. Wong

Full paper (PDF, 204 Kb) | Abstract

*Z*

_{4}. The fact (as shown by Fermat’s Last Theorem) that all the components of a triple cannot simultaneously be an even power

*n*(with ½

*n*even) is illustrated via the spectra of the right-end-digits of the components.

**A remark on an arithmetic function. Part 3**

*Original research paper. Pages 23—27*

Krassimir Atanassov

Full paper (PDF, 126 Kb) | Abstract

*φ*and

*σ*(see, e.g. ). With respect to these research, a new function was defined in and some of its properties were discussed there. Here we shall continue this research.

**Volume 15**▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4