Equivalence of the filament and overlap graphs of subtrees of limited trees
نویسندگان
چکیده
The overlap graphs of subtrees of a tree are equivalent to subtree filament graphs, the overlap graphs of subtrees of a star are cocomparability graphs, and the overlap graphs of subtrees of a caterpillar are interval filament graphs. In this paper, we show the equivalence of many more classes of subtree overlap and subtree filament graphs, and equate them to classes of complements of cochordal-mixed graphs. Our results generalize the previously known results mentioned above.
منابع مشابه
Subtree filament graphs are subtree overlap graphs
We show that the class of intersection graphs of subtree filaments in a tree is identical to the class of overlap graphs of subtrees in a tree.
متن کاملThe second geometric-arithmetic index for trees and unicyclic graphs
Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
متن کاملCaterpillar Tolerance Representations
Various families of tolerance graphs of subtrees for specific families of host trees and tolerance functions have been successfully characterized. For example, chordal graphs are intersection (tolerance 1) graphs of subtrees of general trees, see [2], [5], and [8]. Intersection graphs of subtrees of a path are those that are chordal and do not contain an asteroidal triple, see [7]. We denote by...
متن کاملLeap Zagreb indices of trees and unicyclic graphs
By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...
متن کاملThe Subtree Size Profile of Bucket Recursive Trees
Kazemi (2014) introduced a new version of bucket recursive trees as another generalization of recursive trees where buckets have variable capacities. In this paper, we get the $p$-th factorial moments of the random variable $S_{n,1}$ which counts the number of subtrees size-1 profile (leaves) and show a phase change of this random variable. These can be obtained by solving a first order partial...
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 & Theoretical Computer Science
دوره 19 شماره
صفحات -
تاریخ انتشار 2017