在這篇論文中，我們探討圖的交集表示之參數。在一圖形之交集表示中，每一點都能從一毛蟲（caterpillar）中分配到至多t個星（star），我們稱此表示為t-線星表示。我們稱此最小的t使得此圖形有一t-線星表示為此圖形的線星數。而線星數為1的圖形，則稱為線星圖。在這篇論文中，我們找出線星圖所不能包含的子圖，即線星圖為1的特徵。 / In this thesis, we study intersection parameters for graphs. We introduce linear star number of a graph G, which is the minimum t such that G is the intersection graph of unions of t stars of a host tree that is a caterpillar. The graphs with linear star number 1 are called linear graphs. This thesis is to characterize graphs which are linear substar graphs by providing forbidden induced subgraphs.