Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 3 of 3
Full-Text Articles in Education
Eccentricity Sum In Trees, Heather Smith, Laszlo A. Szekely, Hua Wang
Eccentricity Sum In Trees, Heather Smith, Laszlo A. Szekely, Hua Wang
Department of Mathematical Sciences Faculty Publications
The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.
Tight Super-Edge-Graceful Labelings Of Trees And Their Applications, Alex Collins, Colton Magnant, Hua Wang
Tight Super-Edge-Graceful Labelings Of Trees And Their Applications, Alex Collins, Colton Magnant, Hua Wang
Department of Mathematical Sciences Faculty Publications
The concept of graceful labeling of graphs has been extensively studied. In 1994, Mitchem and Simoson introduced a stronger concept called super-edge-graceful labeling for some classes of graphs. Among many other interesting pioneering results, Mitchem and Simoson provided a simple but powerful recursive way of constructing super-edge-graceful trees of odd order. In this note, we present a stronger concept of “tight” super-edge-graceful labeling. Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels. This concept enables us to recursively construct tight super-edge-graceful trees of any order. As applications, we provide …
Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang
Functions On Adjacent Vertex Degrees Of Trees With Given Degree Sequence, Hua Wang
Department of Mathematical Sciences Faculty Publications
In this note we consider a discrete symmetric function f(x, y) where f(x; a) + f(y, b) ≥ f(y, a) + f(x, b) for any x ≥ y and a ≥ b, associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as Σ uv∈E(T) f(deg(u), deg(v)), are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randić index follow as corollaries. The extremal structures for …