Strongly simplicial vertices of powers of trees
نویسندگان
چکیده
For a tree T and an integer k 1, it is well known that the kth power T k of T is strongly chordal and hence has a strong elimination ordering of its vertices. In this note we obtain a complete characterization of strongly simplicial vertices of T k , thereby characterizing all strong elimination orderings of the vertices of T k . © 2007 Elsevier B.V. All rights reserved.
منابع مشابه
Simplicial Powers of Graphs
In a graph, a vertex is simplicial if its neighborhood is a clique. For an integer k ≥ 1, a graph G = (VG, EG) is the k-simplicial power of a graph H = (VH , EH) (H a root graph of G) if VG is the set of all simplicial vertices of H , and for all distinct vertices x and y in VG, xy ∈ EG if and only if the distance inH between x and y is atmost k. This concept generalizes k-leaf powers introduce...
متن کاملComplete graphs: the space of simplicial cones, and their path tree representation
Let G be a complete graph with n+ 1 vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with the graph. Motivated by the above, we take here a closer look at the geometry of the simplicial cones associated with the graph, and the role played by those simp...
متن کاملOn Leaf Powers
For an integer k, a tree T is a k-leaf root of a finite simple undirected graph G = (V,E) if the set of leaves of T is the vertex set V of G and for any two vertices x, y ∈ V , x 6= y, xy ∈ E if and only if the distance of x and y in T is at most k. Then graph G is a k-leaf power if it has a k-leaf root. G is a leaf power if it is a k-leaf power for some k. This notion was introduced and studie...
متن کاملOn a special class of Stanley-Reisner ideals
For an $n$-gon with vertices at points $1,2,cdots,n$, the Betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. In this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and Betti numbers of the $S$-module $S/I$ where $S=K[x_{1},cdots, x_{n}]$ and $I$ is the associated ideal to ...
متن کاملShellability of Complexes of Trees
A very interesting abstract simplicial complex T (k) n has faces in bijection with the trees with at most n interior vertices, all of which have degrees at least k+2 and are congruent to 2 mod k, and whose leaves are labelled by the distinct integers in [0, 1, ..., m], where m+1 :=nk+2 is the number of leaves (n 0, k 1). Thus the facets of T n correspond to the leaf-labelled trees with n interi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 307 شماره
صفحات -
تاریخ انتشار 2007