| Summary: | 碩士 === 國立東華大學 === 應用數學系 === 103 === Let G be a graph and f : V (G) → N be a coloring on G. Define f(G)=∑_(x∈V(G))f(x).Suppose for all α∈{1,2,...,f(G)} there is a connected subgraph H of G, that ∑_(x∈V(H))f(x)=α , then f is said to be an IC-coloring of G.And the IC-index M(G) is defined as M(G) = max{f(G)|f is an IC-coloring of G}.
Let us focus on the case that G = P_n, a path of length n. Previous results
gives us the upper bound n(n+1)/2 -1 of M(P_n), which is a loose estimation. In
this study,we introduce a new approach, exploiting the property of repeat-
number, to make a tighter estimation of the upper bound of M(P_n),that
M(Pn) <= n(n+1)/2 − 23 if n <= 14.
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