On the adjacent eccentric distance sum of graphs
Halina Bielak; Katarzyna Wolska
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica (2014)
- Volume: 68, Issue: 2
- ISSN: 0365-1029
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topHalina Bielak, and Katarzyna Wolska. "On the adjacent eccentric distance sum of graphs." Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica 68.2 (2014): null. <http://eudml.org/doc/289824>.
@article{HalinaBielak2014,
abstract = {In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph $G$ is defined as\[\xi ^\{sv\} (G)= \sum \_\{v\in V(G)\}\{\frac\{\varepsilon (v) D(v)\}\{deg(v)\}\},\]
where $\varepsilon (v)$ is the eccentricity of the vertex $v$, $deg(v)$ is the degree of the vertex $v$ and\[D(v)=\sum \_\{u\in V(G)\}\{d(u,v)\}\]
is the sum of all distances from the vertex $v$.},
author = {Halina Bielak, Katarzyna Wolska},
journal = {Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica},
keywords = {},
language = {eng},
number = {2},
pages = {null},
title = {On the adjacent eccentric distance sum of graphs},
url = {http://eudml.org/doc/289824},
volume = {68},
year = {2014},
}
TY - JOUR
AU - Halina Bielak
AU - Katarzyna Wolska
TI - On the adjacent eccentric distance sum of graphs
JO - Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
PY - 2014
VL - 68
IS - 2
SP - null
AB - In this paper we show bounds for the adjacent eccentric distance sum of graphs in terms of Wiener index, maximum degree and minimum degree. We extend some earlier results of Hua and Yu [Bounds for the Adjacent Eccentric Distance Sum, International Mathematical Forum, Vol. 7 (2002) no. 26, 1289–1294]. The adjacent eccentric distance sum index of the graph $G$ is defined as\[\xi ^{sv} (G)= \sum _{v\in V(G)}{\frac{\varepsilon (v) D(v)}{deg(v)}},\]
where $\varepsilon (v)$ is the eccentricity of the vertex $v$, $deg(v)$ is the degree of the vertex $v$ and\[D(v)=\sum _{u\in V(G)}{d(u,v)}\]
is the sum of all distances from the vertex $v$.
LA - eng
KW -
UR - http://eudml.org/doc/289824
ER -
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