Covering Walks in Graphs is aimed at researchers and graduate
students in the graph theory community and provides a comprehensive
treatment on measures of two well studied graphical properties,
namely Hamiltonicity and traversability in graphs. This text looks
into the famous K nigsberg Bridge Problem, the Chinese Postman
Problem, the Icosian Game and the Traveling Salesman Problem as
well as well-known mathematicians who were involved in these
problems. The concepts of different spanning walks with examples
and present classical results on Hamiltonian numbers and upper
Hamiltonian numbers of graphs are described; in some cases, the
authors provide proofs of these results to illustrate the beauty
and complexity of this area of research. Two new concepts of
traceable numbers of graphs and traceable numbers of vertices of a
graph which were inspired by and closely related to Hamiltonian
numbers are introduced. Results are illustrated on these two
concepts and the relationship between traceable concepts and
Hamiltonian concepts are examined. Describes several variations of
traceable numbers, which provide new frame works for several
well-known Hamiltonian concepts and produce interesting new
results.
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