t-Path Sigraphs

10.6988/TOJMS.201011.0433

P. Siva Kota Reddy

Sigraphs ； Balance ； Switching ； t-Path sigraphs ； Negation of a sigraph

Tamsui Oxford Journal of Mathematical Sciences

26卷4期（2010 / 11 / 01）

433 - 441

英文

Given a sigraph S and a positive integer t, the t-path sigraph (S)(subscript t) of S is formed by taking a copy of the vertex set V (S) of S, joining two vertices u and v in the copy by a single edge e=uv whenever there is a u-v path of length t in S and then by defining its sign to be-whenever in every u-v path of length t in S all the edges are negative. In this paper, we introduce a variation of the concept of t-path sigraphs studied above. The motivation stems naturally from one's mathematically inquisitiveness as to ask why not define the sign of an edge e=uv in (S) (subscript t) as the product of the signs of the vertices u and v in S. It is shown that for any sigraph S, its t-path sigraph (S) (subscript t) is balanced. We then give structural characterization of t-path sigraphs. Further, in this paper we characterize sigraphs which are switching equivalent to their 2(3)-path sigraphs.