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...

In this paper we study finding the $(k,l)$-core problem on a tree which the vertices have positive or negative weights. Let $T=(V,E)$ be a tree. The $(k,l)$-core of $T$ is a subtree with at most $k$ leaves and with a diameter of at most $l$ which the sum of the weighted distances from all vertices to this subtree is minimized. We show that, when the sum of the weights of vertices is negative, t...

Abstract We present new, faster pseudopolynomial time algorithms for the k - Subset Sum problem, defined as follows: given a set Z of n positive integers and targets $$t_1, \ldots , t_k$$ t 1 , … k </mml:math...