ISSN 1234-3099 (print version)
ISSN 2083-5892 (electronic version)
SCImago Journal Rank (SJR) 2018: 0.763
Rejection Rate (2018-2019): c. 84%
Article in press
Branch-weight unique trees
Discussiones Mathematicae Graph Theory
A branch at a vertex $x$ in a tree is a maximal subtree containing $x$ as an
endvertex. The branch-weight of $x$ is the maximum number of edges in any
branch at $x$. The branch-weight sequence of a tree is the multiset consisting
of the branch-weights of all vertices arranged in nonincreasing order.
Non-isomorphic trees may have the same branch-weight sequence. A tree $T$ is
said to be branch-weight unique in a family of trees if $T$ is uniquely
determined in the family by its branch-weight sequence. A spider is a tree in
which exactly one vertex has degree exceeding two. It is known that spiders are
branch-weight unique in the family of spiders but not in the family of all trees.
In this study, a necessary and sufficient condition is obtained whereby a spider
may be branch-weight unique in the family of all trees. Moreover, two types of
trees are proposed to be branch-weight unique in the family of all trees.
branch-weight, branch-weight sequence, branch-weight unique,