Let G be a connected graph and g non-negative integer. A vertex set S of is called g-extra cut if G−S disconnected each component has at least g+1 vertices. The connectivity the minimum cardinality one cut. For two graphs G1=(V1,E1) G2=(V2,E2), strong product G1⊠G2 defined as follows: its V1×V2 edge {(x1,x2)(y1,y2)|x1=x2 y1y2∈E2; or y1=y2 x1x2∈E1; x1x2∈E1 y1y2∈E2}, where (x1,x2),(y1,y2)∈V1×V2. ...

Non-parametric estimation of a survival function from left truncated data subject to right censoring has been extensively studied in the literature. It is commonly assumed in such studies that the lifetime variables are a sample of independent and identically distributed random variables from the target population. This assumption is often prone to failure in practical studies. For instance, wh...

Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...