In this paper, we study the problem of computing a minimum cost Steiner tree subject to a weight constraint in a Halin graph where each edge has a nonnegative integer cost and a nonnegative integer weight. We prove the NP-hardness of this problem and present a fully polynomial time approximation scheme for this NP-hard problem.

In this paper, we improve the existing bounds [2] for 2-dipath and oriented L(2, 1) span for the class of planar graphs with girth 5, 11, 16, cactus, wheels and leaf independent Halin graphs. Some of these bounds are tight.

The difference of Zagreb indices a graph G is defined as ΔM(G)=∑u∈V(G)(d(u))2−∑uv∈E(G)d(u)d(v), where d(x) denotes the degree vertex x in G. A Halin that results from plane tree T without vertices two and with at least one three such all leaves are joined through cycle C embedded order. In this paper, we establish both lower upper bounds on for general graphs some special fewer inner vertices. ...

A star k-edge coloring is a proper edge such that there are no bichromatic paths or cycles of length four. The smallest integer k G admits the chromatic index G. Deng et al. [5], and Bezegová [1] independently proved tree at most ⌊3Δ2⌋, bound sharp. Han [8] strengthened result to list version index, ⌊3Δ2⌋ also sharp upper for trees. generalized Halin graph plane consists embedding T with Δ(T)≥3...

Oriented chromatic number of an oriented graph G is the minimum order of an oriented graph H such that G admits a homomorphism to H . The oriented chromatic number of an unoriented graph G is the maximal chromatic number over all possible orientations of G. In this paper, we prove that every Halin graph has oriented chromatic number at most 8, improving a previous bound by Hosseini Dolama and S...

Professor Rudolf Korinthenberg is medical director of the Department for Child Neurology and chief of the muscle clinic at the Center for Pediatrics and Youth Medicine at the University of Freiburg in Germany. On 15 February 2006, Dr. Guenter Scheuerbrandt spoke to Professor Korinthenberg about the possibilities which are now available to the parents and the doctors for treating and managing a ...