In this paper, first, a 3rd-dimensional vertex measurable graphs G is defined, which is an extension of the concept that was introduced in [3]. G = G1 × G2 × G3 is a graph defined over algebra ζ1 ×ζz...In this paper, first, a 3rd-dimensional vertex measurable graphs G is defined, which is an extension of the concept that was introduced in [3]. G = G1 × G2 × G3 is a graph defined over algebra ζ1 ×ζz × ζ3, which consists of all vertex sets that produce sub graphs of G. G1,G2, and G3 are three simple graphs, provided that (G1,ζ1),(G2,ζz), and (G3,ζ3) are three vertex measure spaces. Second, in order to maximize the edge's set, we present an alternative version of the definition of two-dimension Cartesian product of vertex measurable graphs that was given in [3], with preserving the same properties of the graphs and sub graphs that were illustrated.展开更多
文摘In this paper, first, a 3rd-dimensional vertex measurable graphs G is defined, which is an extension of the concept that was introduced in [3]. G = G1 × G2 × G3 is a graph defined over algebra ζ1 ×ζz × ζ3, which consists of all vertex sets that produce sub graphs of G. G1,G2, and G3 are three simple graphs, provided that (G1,ζ1),(G2,ζz), and (G3,ζ3) are three vertex measure spaces. Second, in order to maximize the edge's set, we present an alternative version of the definition of two-dimension Cartesian product of vertex measurable graphs that was given in [3], with preserving the same properties of the graphs and sub graphs that were illustrated.