圖的全星數

Abstract

A multiple-star representation of a simple graph G assigns each vertex a union of stars in a host tree, such that vertices are adjacent if and only if their assigned sets intersect. The total star number S(G) is the minimum of the total number of stars used in any such representation of G. We obtain the maximum value of S(G) for m-edge connected graphs: m + 1, n-vertex graphs: [n² + 1)/ 4], and n-vertex outer-planar graphs: [3n /2-l]