DEPTH AND STANLEY DEPTH OF THE EDGE IDEALS OF SOME m-LINE GRAPHS AND m-CYCLIC GRAPHS WITH A COMMON VERTEX

Romanian Journal of Mathematics and Computer Science

GUANGJUN ZHU¹ 

[1] School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China, E-mail address: [e-mail];

关键词: Stanley depth;    depth;    Stanley conjecture;    edge ideal;   

DOI  :  

来源: DOAJ

【 摘 要 】

We give some precise formulas for the depth of the quotient rings of the edge ideals associated to a graph consisting, either of the union of some line graphs L_{3r_1}},...,L_{3r_{k_1}}, L_{3s_1+1}, ...,L_{3s_{k_2}+1} and L_{3t_1+2},...,L_{3t_{k_3}+2} or of the union of cycle graphs C_{3r_1},...,C_{3r_{k_1}}, C_{3s_1+1},..., C_{3s_{k_2}+1}and C_{3t_1+2},...,;C_{3t_{k_3}+2}, with a common vertex. We also give some tight bounds for their Stanley depths.

【 授权许可】

Unknown