We determine the minimum sum–connectivity index of bicyclic graphs with n vertices and matching number m, where 2 ≤ m ≤ ⌊n2 ⌋, the minimum and the second minimum, as well as the maximum and the second maximum sum–connectivity indices of bicyclic graphs with n ≥ 5 vertices. The extremal graphs are characterized. MSC 2000: 05C90; 05C35; 05C07

A set of sets is called a family. Two families and B are said to be cross-intersecting if each member intersects B. For any two integers n k with 1≤k≤n, let ([n]≤k) denote the family subsets [n]={1,…,n} that have at most elements. We show non-empty subfamily ([n]≤r), ([n]≤s), r≤s, cross-intersecting, then|A|+|B|≤1+∑i=1s((ni)−(n−ri)), equality holds A={[r]} in ([n]≤s) intersect [r].

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

BACKGROUND In carnitine palmitoyltransferase I (CPT-I) deficiency (MIM 255120), free carnitine can be increased with no pathologic acylcarnitine species detectable. As inclusion of CPT-I deficiency in high-risk and newborn screening could prevent potentially life-threatening complications, we tested whether CPT-I deficiency might be diagnosed by electrospray ionization-tandem mass spectrometry ...