CAJ | 학술논문

G是一个简单图，矩阵Q（G）＝ D（G）＋ A（G）表示图G的无符号拉普拉斯矩阵，其中 D（G）和A（G）分别为对角元素为图G顶点度的对角阵和图G的邻接矩阵，矩阵 L（G）＝ D（G）-D（G）记为图 G的拉普拉斯矩阵。若一个图的拉普拉斯矩阵的特征值全为整的，则称此图为 L整图，Q整图类似定义。本文针对两类联图G1∨· G2和G1宠G2，分别得到了它们的Q谱和L 谱，进一步得到了Q整谱图和L 整谱图的一些无限类。
G시일개간단도，구진Q（G）＝ D（G）＋ A（G）표시도G적무부호랍보랍사구진，기중 D（G）화A（G）분별위대각원소위도G정점도적대각진화도G적린접구진，구진 L（G）＝ D（G）-D（G）기위도 G적랍보랍사구진。약일개도적랍보랍사구진적특정치전위정적，칙칭차도위 L정도，Q정도유사정의。본문침대량류련도G1∨· G2화G1총G2，분별득도료타문적Q보화L 보，진일보득도료Q정보도화L 정보도적일사무한류。
Let G be a simple graph .The matrix Q(G)= D(G)+ A(G) is the signless Laplacian matrix of G ,where D(G) and A(G) is the diagonal matrix of vertex degrees and the adjacency matrix of G ,respectively .The Laplacian matrix of G is the matrix L(G)= D(G)-A(G) .A graph iscalled L-integral (resp .Q-integral) if its (signless) Laplacian spectrum consists entire-ly of integers .Let G1 and G2 be two graphs ,and S(G) be the subdivision graph of G .Then the Svertex join of G1 and G2 ,denoted by G1 ∨· G2 is obtained from S(G1 ) and G2 by joining each verti-ces of G1 to each vertices of G2 .The Sedge join of G1 with G2 ,denoted by G1 ∨ G2 is obtained from S(G1 ) and G2 by joining all vertices of S(G1 ) corresponding to the edges of G1 with all vertices of G2 .In this paper we obtain the Q-spectra and L-spectra of these two joins of graphs w hen G1 and G2 are regular graphs . As an application ,some infinite families of Q-integral graphs and L-integral graphs are obtained .