A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph G, denoted sχ′(G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a plane graph constructed from a tree T without vertice...

A Halin graph the union of a tree with no degree-2 vertices and a cycle on the leaves of the tree. This paper examines the problem of laying out Halin graphs using stacks and queues. A k-stack (k-queue) layout of a graph consists of a linear ordering of the vertices along with an assignment of each edge to one of k stacks (queues). The ordering and the edge assignments must be made such that if...

We show that every 2-connected (2)-Halin graph is Hamiltonian.

We show that there exists a linear-time algorithm that computes the strong chromatic index of Halin graphs.

We derive an O(n)-time algorithm for calculating the genus distribution of a given 3-regular Halin graph G; that is, we calculate the sequence of numbers g0(G), g1(G), g2(G), . . . on the respective orientable surfaces S0, S1, S2, . . . . Key topological features are a quadrangular decomposition of plane Halin graphs and a new recombinant-strands reassembly process that fits pieces together thr...

We investigate here the hamiltonicity and traceability of a class of polytopes generalizing pyramids, prisms, and polytopes with Halin 1-skeleta.