| Summary: | 碩士 === 東海大學 === 應用數學系 === 101 === Let G = (V (G),E(G)) be a finite simple graph with p = |V (G)| vertices
and q = |E(G)| edges. An antimagic labeling of G is a bijection from
the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums
are pairwise distinct, where the vertex sum at a vertex is the sum of labels
of all edges incident to such vertex. A vertex magic total labeling is a
bijection from V (G) ∪ E(G) to the set of integers 1, 2, · · · , p + q, with the
property that, for every vertex u in V (G), one has f(u)+
Σuv∈E(G) f(uv) = k
for some constant k. On the other hand, for an undirected graph G, a
zero-sum
ow is an assignment of possibly repeated non-zero integers to
the edges such that the sum of the values of all edges incident with each
vertex is zero. In this thesis we study the above graph labeling problems
of magic and antimagic types. In particular, we identify classes of graphs
admitting antimagic labeling and vertex magic total labeling respectively,
which generalize and extend previous results. We also consider zero-sum flow
problems for the hexagonal graphs, for which infinite families of hexagonal
grid graphs with small zero-sum flow numbers are presented.
|
|---|
