Superdominance order and distance of trees with bounded maximum degree

k-forested choosability of graphs with bounded maximum average degree

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

Distance spectral radius of trees with fixed maximum degree

Ela Distance Spectral Radius of Trees with Fixed Maximum Degree∗

Abstract. Distance energy is a newly introduced molecular graph-based analog of the total π-electron energy, and it is defined as the sum of the absolute eigenvalues of the molecular distance matrix. For trees and unicyclic graphs, distance energy is equal to the doubled value of the distance spectral radius. In this paper, we introduce a general transformation that increases the distance spect...

Computing the Quartet Distance Between Evolutionary Trees of Bounded Degree

We present an algorithm for calculating the quartet distance between two evolutionary trees of bounded degree on a common set of n species. The previous best algorithm has running time O(d2n2) when considering trees, where no node is of more than degree d. The algorithm developed herein has running time O(d9n log n)) which makes it the first algorithm for computing the quartet distance between ...

k-forested choosability of graphs with bounded maximum average degree

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...