In this paper we construct for each integer ≥ 11, ≠ 12 15 a pair of trees of order which are not isomorphic but numerically isomeric. We also construct for each even ≥ 12 a pair of 2connected cubic graphs with the same property

The labeling problem considered for this is called face-labeling of the maximal planar or triangular planar graphs in connection with the notion of the . Several triangular planar and maximal planar graphs such as the wheels, the fans etc. have been considered. The face-labeling of maximal...

Given a set of points in a plane, a spanning tree is a set of edges that connects all the points and contains no cycles. If each edge is weighted using the rectilinear distance metric, the rectilinear minimum spanning tree is a tree whose sum of edge weights is minimum. A naive approach to...

Let = () be a graph without isolated vertices. We say that ⊂ is a if every vertex has a neighbor in . Let () denote the minimum cardinality of a total dominating set of . We prove that if is a graph of order and minimum degree at least 3 then () ≤ /2. If equality holds then must be 3-regular...

Let denote the class of intersection graphs of linear 3-uniform hypergraphs. In this paper a polynomial algorithm solving the recognition problem for the graphs with bound on minimum vertex degree δ()≥ 13 is proposed

This paper deals with the problem of constructing directed trees of optimal weight and root with depth at most (||) (called − ). We first prove that the maximization and the minimization versions are equal-approximable under the that measures how the value of an approximate solution is placed...

This paper deals with the problem of constructing directed trees of optimal weight and root with depth at most (||) (called – ). We first prove that the maximization and the minimization versions are equal-approximable under the that measures how the value of an approximate solution is placed...

A dual-Eulerian graph is a plane graph which has an ordering defined on its edge set which forms simultaneously an Euler circuit in the graph and an Euler circuit in the dual graph. Dual-Eulerian graphs were defined and studied in the context of silicon optimization of cmos layouts. They are...

The possibilities for circuits of length 4 to appear together in a cubic bigraph are classified. That has consequences on the structure of minimally 1-factorable regular bigraphs, i.e. those in which each 1-factor lies in precisely one 1-factorization. We characterize minimally 1-factorable...