TY - JOUR
T1 - Shapley Distance and Shapley Index for Some Special Graphs
AU - Gu, Zhendong
AU - Zhou, Shuming
AU - Liu, Jiafei
AU - Zhou, Qianru
AU - Wang, Dajin
N1 - Publisher Copyright:
© 2020 World Scientific Publishing Company.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2020/12
Y1 - 2020/12
N2 - The Shapley distance in a graph is defined based on Shapley value in cooperative game theory. It is used to measure the cost for a vertex in a graph to access another vertex. In this paper, we establish the Shapley distance between two arbitrary vertices for some special graphs, i.e., path, tree, cycle, complete graph, complete bipartite, and complete multipartite graph. Moreover, based on the Shapley distance, we propose a new index, namely Shapley index, and then compare Shapley index with Wiener index and Kirchhoff index for these special graphs. We also characterize the extremal graphs in which these three indices are equal.
AB - The Shapley distance in a graph is defined based on Shapley value in cooperative game theory. It is used to measure the cost for a vertex in a graph to access another vertex. In this paper, we establish the Shapley distance between two arbitrary vertices for some special graphs, i.e., path, tree, cycle, complete graph, complete bipartite, and complete multipartite graph. Moreover, based on the Shapley distance, we propose a new index, namely Shapley index, and then compare Shapley index with Wiener index and Kirchhoff index for these special graphs. We also characterize the extremal graphs in which these three indices are equal.
KW - Kirchhoff index
KW - Shapley distance
KW - Shapley index
KW - Shapley value
KW - Wiener index
UR - http://www.scopus.com/inward/record.url?scp=85099079886&partnerID=8YFLogxK
U2 - 10.1142/S0129626420500127
DO - 10.1142/S0129626420500127
M3 - Article
AN - SCOPUS:85099079886
SN - 0129-6264
VL - 30
JO - Parallel Processing Letters
JF - Parallel Processing Letters
IS - 4
M1 - 2050012
ER -