The strong product G1 £G2 of graphs G1 and G2 is the graph with V (G1) × V (G2) as the vertex set, and two distinct vertices (x1, x2) and (y1, y2) are adjacent whenever for each i ∈ {1, 2} either xi = yi or xiyi ∈ E(Gi). In this note we show that for two connected graphs G1 and G2 the edge-connectivity λ(G1£G2) equals min{δ(G1£ G2), λ(G1)(|V (G2)|+2|E(G2)|), λ(G2)(|V (G1)|+2|E(G1)|)}. In additi...

Three soils of different content gypsum and lime were selected, the first soil (G1) second (G3), obtained near fields Faculty Agriculture, Tikrit University. As for third (G5), was taken from AL- alam Village side east city to a depth (0-10)cm. proportions 5%, 15%, 25%, 20%, 10% G1, G3, G5, respectively. Ferrous sulfate added as source iron ions three in following (0,10,25,50,100,150,250,500,75...

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...

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 ...

Two phosphonium-derived ionic liquids: trihexyltetradecylphosphonium bis(2-ethylhexyl)phosphate (IL1) and tricyanomethanide (IL2) were used as additives in lithium complex- (G1) anhydrous calcium-based (G2) greases at 5 wt%. Friction torque wear tests performed using a modified four-ball machine for testing rolling bearings order to determine the friction reducing properties of these grease sam...