Motivated by problems in radio channel assignments, we consider radio k-labelings of
graphs. For a connected graph G and an integer k≥ 1, a linear radio k-labeling of G is an …

For a connected graph $ G $ of order $ n\ge 3$ and an ordering $ s\: v_1 $, $ v_2,\cdots, v_n
$ of the vertices of $ G $, $ d (s)=\sum _ {i= 1}^{n-1} d (v_i, v_ {i+ 1}) $, where $ d (v_i, v_ {i+ …

For a nontrivial connected graph G of order n and a linear ordering s: v 1, v 2,…, vn of
vertices of G, define d (s)= ∑ i= 1^ n-1 d (v_i, v_ i+ 1). The traceable number t (G) of a graph …

In the paper, we study the hamiltonian numbers in digraphs. A hamiltonian walk of a digraph
D is a closed spanning directed walk with minimum length in D. The length of a hamiltonian …

Let G be a connected graph, and let d (u, v) denote the distance between vertices u and v in
G. For any cyclic ordering π of V (G), π=(v1, v2,···, vn, vn+ 1) where vn+ 1= v1, let d (π)= n∑ …

For the study of hamiltonicity of graphs and digraphs, Goodman and Hedetniemi introduced
the concept of Hamiltonian number. The Hamiltonian number h (D) of a digraph D is the …

A hamiltonian walk of a digraph is a closed spanning directed walk with minimum length in
the digraph. The length of a hamiltonian walk in a digraph D is called the hamiltonian …

A hamiltonian walk in a digraph D is a closed spanning directed walk of D with minimum
length. The length of a hamiltonian walk in D is called the hamiltonian number of D, and is …

INTERPOLATION AND EXTREMAL THEOREMS: THE HAMILTONIAN NUMBER OF CUBIC
GRAPHS A THESIS BY SERMSRI THAITHAE Presented in Partial Fu Page 1 …

For a connected graph G of order n≥ 3 and a cyclic ordering sc: v 1, v2,..., vn, v n+ 1= v1 of
vertices of G, the number d (sc) is defined by d (sc)= i= 1n d (vi, vi+ 1), where d (vi, vi+ 1) is …