| Summary: | 碩士 === 國立臺北商業技術學院 === 資訊與決策科學研究所 === 102 === Let G be a graph with vertex set V(G) and edge set E(G), respectively. We denote by I(G)={(v,e): v Belong V(G),e Belong E(G)and v is an end-vertex of e} the set of incidences of G and investigate the following graph labeling problem. An incidence ranking of a graph G is a mapping f:I(G) are integers such that for any path between two distinct incidences i,j Belong I(G) with f(i)=f(j), there exists an incidence x in the path with f(x)>f(i). An incidence ranking f is a k-incidence ranking, if k=max{f(i):i Belong I(G). The incidence ranking number of G, denoted Xir(G), is defined by Xir(G)=min{k are integers: f is a k-incidence ranking of G. The incidence ranking problem
is to determine the incidence ranking number of a given graph. In this thesis, we obtain the incidence ranking numbers of paths, cycles and grids Pm X Pn for m=2,3. Moreover, upper bounds of Xir(Gm,n) for m=4,5,6
are also acquired.
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