The search of spanning trees with interesting disjunction properties has led to the introduction of edge-disjoint spanning trees, independent spanning trees and more recently completely independent spanning trees. We group together these notions by defining (i, j)-disjoint spanning trees, where i (j, respectively) is the number of vertices (edges, respectively) that are shared by more than one ...

A spanning tree of a graph G is a connected acyclic spanning subgraph of G. We consider enumeration of spanning trees when G is a 2-tree, meaning that G is obtained from one edge by iteratively adding a vertex whose neighborhood consists of two adjacent vertices. We use this construction order both to inductively list the spanning trees without repetition and to give bounds on the number of the...

a spanning tree of graph g is a spanning subgraph of g that is a tree. in this paper, we focusour attention on (n,m) graphs, where m = n, n + 1, n + 2 and n + 3. we also determine somecoefficients of the laplacian characteristic polynomial of fullerene graphs.

Mitigation of atmospheric pollution has been a topic of concern over the past decades. In this study, tree rings have been used to reconstruct past climates as well as to assess the effects of recent climatic and environmental changes on tree growth. Vehicular emission is one of the major sources of pollutants in the atmosphere and this study focused on the Haatso-Atomic road which over the yea...

Preface The research on spanning trees has been one of the most important areas in algorithm design. People who are interested in algorithms will find this book informative and inspiring. The new results are still accumulating, and we try to make clear the whole picture of the current status and future developments. This book is written for graduate or advanced undergraduate students in compute...