The (k − 1)-fault diameter Dk(G) of a k-connected graph G is the maximum diameter of G− F for any F ⊂ V (G) with |F | < k. Krishnamoorthy and Krishnamurthy first proposed this concept and gave Dκ(G1)+κ(G2)(G1 ×G2) Dκ(G1)(G1)+ Dκ(G2)(G2) when κ(G1 ×G2)= κ(G1)+ κ(G2), where κ(G) is the connectivity of G. This paper gives a counterexample to this bound and establishes Dk1+k2(G1 × G2) Dk1(G1) +Dk2 ...

As weak forms of continuity in topological spaces, weak continuity [I], quasi continuity [2], semi continuity [3] and almost continuity in the sense of Husain [4] are well-known. Recently, the following four weak forms of continuity have been introduced: weak quasi continuity [5], faint continuity [6], subweak continuity [7] and almost weak continuity [8]. These four weak forms of continuity ar...

Two graphs G1 and G2, each on n vertices, pack if there exists a bijection f from V (G1) onto V (G2) such that uv ∈ E(G1) only if f (u)f (v) ∉ E(G2). In 2014, Alon and Yuster proved that, for sufficiently large n, if |E(G1)| < n − δ(G2) and ∆(G2) ≤ √ n/200, then G1 and G2 pack. In this paper, we characterize the pairs of graphs for which the theorem of Alon and Yuster is sharp.We also prove the...

Background: The combination of doxorubicin (DOX) with paclitaxel (PTX) effectively treats breast cancer (BC). However,DOX-associated cardiotoxicity (CTX) is aggravated by the use PTX. Consensus lacking about which drug sequence involves most CTX. Objectives: To evaluate whether DOX followed PXT or reverse has greatest cardiotoxic potential in treatment BC. Methods: Prospective study women prima...

Let WQ = Proj(Q[g2' g3' X, Y, ZJI(homogeneous ideal generated by y 2Z + 4X3 g2XZ2 g3Z3». This is said to be the Weierstrass Family over the field Q. Then the first homology with compact supports of the Weierstrass Family is computed explicitly, i.e., it is generated by {C-kdX 1\ dYh .. , and {XC-kdX 1\ dYh .. 1 over the ring Q[g2' g3]' where C is a polynomial y 2 4X3 + g2 X + g3' When one tenso...