Geodesic
Extremal properties of distance-based graph invariants for $k$-trees
Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 41-66

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Sharp bounds on some distance-based graph invariants of $n$-vertex $k$-trees are established in a unified approach, which may be viewed as the weighted Wiener index or weighted Harary index. The main techniques used in this paper are graph transformations and mathematical induction. Our results demonstrate that among $k$-trees with $n$ vertices the extremal graphs with the maximal and the second maximal reciprocal sum-degree distance are coincident with graphs having the maximal and the second maximal reciprocal product-degree distance (and similarly, the extremal graphs with the minimal and the second minimal degree distance are coincident with graphs having the minimal and the second minimal eccentricity distance sum).
DOI : 10.21136/MB.2017.0011-16
Classification : 34B16, 34C25
Keywords: distance-based graph invariant; $k$-tree; simplicial vertex; sharp bound 
@article{10_21136_MB_2017_0011_16,
     author = {Zhang, Minjie and Li, Shuchao},
     title = {Extremal properties of distance-based graph invariants for $k$-trees},
     journal = {Mathematica Bohemica},
     pages = {41--66},
     publisher = {mathdoc},
     volume = {143},
     number = {1},
     year = {2018},
     doi = {10.21136/MB.2017.0011-16},
     mrnumber = {3778049},
     zbl = {06861591},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0011-16/}
}
TY  - JOUR
AU  - Zhang, Minjie
AU  - Li, Shuchao
TI  - Extremal properties of distance-based graph invariants for $k$-trees
JO  - Mathematica Bohemica
PY  - 2018
SP  - 41
EP  - 66
VL  - 143
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0011-16/
DO  - 10.21136/MB.2017.0011-16
LA  - en
ID  - 10_21136_MB_2017_0011_16
ER  - 
%0 Journal Article
%A Zhang, Minjie
%A Li, Shuchao
%T Extremal properties of distance-based graph invariants for $k$-trees
%J Mathematica Bohemica
%D 2018
%P 41-66
%V 143
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2017.0011-16/
%R 10.21136/MB.2017.0011-16
%G en
%F 10_21136_MB_2017_0011_16
Zhang, Minjie; Li, Shuchao. Extremal properties of distance-based graph invariants for $k$-trees. Mathematica Bohemica, Tome 143 (2018) no. 1, pp. 41-66. doi: 10.21136/MB.2017.0011-16

Cité par Sources :