首页|On the resistance diameters of graphs and their line graphs
On the resistance diameters of graphs and their line graphs
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NSTL
Elsevier
Let G = (V(G), E(G)) be a graph with vertex set V(G) and edge set E(G). The line graph L-G of G is the graph with E(G) as its vertex set and two vertices of L-G are adjacent in L-G if and only if they have a common end-vertex in G. The resistance distance R-G(x, y) between two vertices x, y of G is equal to the effective resistance between the two vertices in the corresponding electrical network in which each edge of G is replaced by a unit resistor. The resistance diameter D-r(G) of G is the maximum resistance distance among all pairs of vertices of G. In this paper, it was shown that the resistance diameter of the line graph of a tree or unicyclic graph is no more than that of its initial graph by utilizing series and parallel principles, the principle of elimination and star-mesh transformation in electrical network theory. And experiment also indicated that the inequality D-r(L-G) <= D-r(G) is true for every simple nonempty connected graph G with less than 12 vertices. Thus it was conjectured that D-r(L-G) <= D-r(G) for every simple nonempty connected graph G. (C) 2021 Elsevier B.V. All rights reserved.
NSTL
Elsevier
