Automorphism Group of Some A-Join of Graphs

چکیده مقاله

For a simple graph A, the A-join G of a set of complete or empty graphs fAaga2V(A) is an another simple graph with the vertex and edge sets f(a;b) j a 2 V(A) & b 2 V(Aa)g and f(a;b)(a0;b0) j aa0 2 E(A) or else a = a0 & bb0 2 E(Aa)g, respectively. This graph is called reduced if NA(a) n fbg = NA(b) n fag, a;b 2V(A) and a 6= b, implies that (i) if ab 62 E(A) then at least Aa or Ab are non-empty; (ii) if ab 2 E(A) then at least one of Aa or Ab are not complete. In this talk, we report our recent results on the automorphism group of reduced completeempty A-join of graphs.