| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 88 === Given a graph G , a proper labeling f of G is an one-to-one function. The bandwidth sum of a graph G , denoted by B_s is defined byB_s=min{sum_{uv in E(G)}|f(u)-f(v)|} , where the minimum is taken for all proper labeling f of G . In this thesis, we study the bandwidth sum problem for the join of k graphs G_{1},G_{2},...,G_{k} , where each G_{i} is a path, cycle, complete graph, or union of isolated vertices. We also study the bandwidth sum for the composition of a path P_{n} with a graph H , where H is a path, cycle, or union of isolated vertices.
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