CAJ | 학술논문

如果一个图的拉普拉斯谱都是由整数构成的，那么这个图称为拉普拉斯整谱图。本文首先刻画了拉普拉斯三圈基图中最长圈的圈长c(H)≤6的整谱图，并且找出这些连通的拉普拉斯三圈基图的整谱图；其次刻画了至少含有一个悬挂点的连通三圈图的拉普拉斯整谱图，最后证明了至少含有一个悬挂点的连通三圈图的拉普拉斯整谱图都是由它们的拉普拉斯谱唯一确定的。
여과일개도적랍보랍사보도시유정수구성적，나요저개도칭위랍보랍사정보도。본문수선각화료랍보랍사삼권기도중최장권적권장c(H)≤6적정보도，병차조출저사련통적랍보랍사삼권기도적정보도；기차각화료지소함유일개현괘점적련통삼권도적랍보랍사정보도，최후증명료지소함유일개현괘점적련통삼권도적랍보랍사정보도도시유타문적랍보랍사보유일학정적。
A graph is a Laplacian integral graph if the Laplacian spectrum consists of integers. In this paper, we find all the Laplacian integer tricyclic base-graphs H with c(H)≤6 where c(H) is the circumference of H. Next we show all the Laplacian integer tricyclic graphs of order n with at least one pendent. Moreover, we show that all the Laplacian integer tricyclic graphs of order n with at least one pendent are determined by their Laplacian spectra.