کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423513 | 1342400 | 2012 | 10 صفحه PDF | دانلود رایگان |
Generalized Fibonacci cube Qd(f) is introduced as the graph obtained from the d-cube Qd by removing all vertices that contain a given binary string f as a substring. In this notation, the Fibonacci cube Îd is Qd(11). The question whether Qd(f) is an isometric subgraph of Qd is studied. Embeddable and non-embeddable infinite series are given. The question is completely solved for strings f of length at most five and for strings consisting of at most three blocks. Several properties of the generalized Fibonacci cubes are deduced. Fibonacci cubes are, besides the trivial cases Qd(10) and Qd(01), the only generalized Fibonacci cubes that are median closed subgraphs of the corresponding hypercubes. For admissible strings f, the f-dimension of a graph is introduced. Several problems and conjectures are also listed.
Journal: Discrete Mathematics - Volume 312, Issue 1, 6 January 2012, Pages 2-11