Graph is an usual representation of relational data, which are ubiquitous in many domains such as molecules, biological and social networks. A popular approach to learning with graph structured data make use kernels, measure the similarity between graphs plugged into a kernel machine support vector machine. Weisfeiler-Lehman (WL) based employ WL labeling scheme extract subtree patterns perform ...

For a tree T $T$ , the mean subtree order of is average . In 1984, Jamison conjectured that decreases by at least 1/3 after contracting an edge in this article we prove conjecture special case contracted pendant edge. From result, have new proof established fact path P n ${P}_{n}$ has minimum among all trees $n$ Moreover, sharp lower bound derived for difference between orders and proper S $S$ ...

Chang, Y.-W., M.S. Jacobson, CL. Monma and D.B. West, Subtree and substar intersection numbers. Discrete Applied Mathematics 44 (1993) 205-220. We introduce the star number [free number] of a graph, being the minimum t such that G is the intersection graph of unions of t substars [subtrees] of a host tree. We study bounds on these parameters, compare them with interval number, and characterize ...

We introduce an approach to learn discriminative visual representations while exploiting external semantic knowledge about object category relationships. Given a hierarchical taxonomy that captures semantic similarity between the objects, we learn a corresponding tree of metrics (ToM). In this tree, we have one metric for each non-leaf node of the object hierarchy, and each metric is responsibl...

We consider the quantity P ( G ) associated with a graph that is defined as probability randomly chosen subtree of spanning. Motivated by conjectures due to Chin, Gordon, MacPhee and Vincent on behaviour this invariant depending edge density, we establish first bounded below positive constant provided minimum degree linear function in number vertices. Thereafter, focus shifted classical Erd?s–R...