TY - UNPB
T1 - Semiregular Trees with Minimal Index
AU - Biyikoglu, Türker
AU - Leydold, Josef
PY - 2009/6/1
Y1 - 2009/6/1
N2 - A semiregular tree is a tree where all non-pendant vertices have the same degree. Belardo et al. (MATCH Commun. Math. Chem. 61(2), pp. 503-515, 2009) have shown that among all semiregular trees with a fixed order and degree, a graph with index is caterpillar. In this technical report we provide a different proof for this theorem. Furthermore, we give counter examples that show that this result cannot be generalized to the class of trees with a given (non-constant) degree sequence.
AB - A semiregular tree is a tree where all non-pendant vertices have the same degree. Belardo et al. (MATCH Commun. Math. Chem. 61(2), pp. 503-515, 2009) have shown that among all semiregular trees with a fixed order and degree, a graph with index is caterpillar. In this technical report we provide a different proof for this theorem. Furthermore, we give counter examples that show that this result cannot be generalized to the class of trees with a given (non-constant) degree sequence.
U2 - 10.57938/27793b26-56cb-4e35-9193-572e8bac1d80
DO - 10.57938/27793b26-56cb-4e35-9193-572e8bac1d80
M3 - WU Working Paper
T3 - Research Report Series / Department of Statistics and Mathematics
BT - Semiregular Trees with Minimal Index
ER -