﻿ On reverse degree distance of unicyclic graphs

# On reverse degree distance of unicyclic graphs

##### نویسندگان
• Z. Du Northeast Normal University
##### چکیده

The reverse degree distance of a connected graph \$G\$ is defined in discrete mathematical chemistry as [ r (G)=2(n-1)md-sum_{uin V(G)}d_G(u)D_G(u), ] where \$n\$, \$m\$ and \$d\$ are the number of vertices, the number of edges and the diameter of \$G\$, respectively, \$d_G(u)\$ is the degree of vertex \$u\$, \$D_G(u)\$ is the sum of distance between vertex \$u\$ and all other vertices of \$G\$, and \$V(G)\$ is the vertex set of \$G\$. We determine the unicyclic graphs of given girth, number of pendant vertices and maximum degree, respectively, with maximum reverse degree distances. We also determine the unicyclic graphs of given number of vertices, girth and diameter with minimum degree distance.

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## on reverse degree distance of unicyclic graphs

the reverse degree distance of a connected graph \$g\$ is defined in discrete mathematical chemistry as [ r (g)=2(n-1)md-sum_{uin v(g)}d_g(u)d_g(u), ] where \$n\$, \$m\$ and \$d\$ are the number of vertices, the number of edges and the diameter of \$g\$, respectively, \$d_g(u)\$ is the degree of vertex \$u\$, \$d_g(u)\$ is the sum of distance between vertex \$u\$ and all other vertices of \$g\$, and \$v(g)\$ is the ...

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## On Reverse Degree Distance of Unicyclic Graphs

The reverse degree distance of a connected graph G is defined in discrete mathematical chemistry as D(G) = 2(n− 1)md− ∑

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## degree resistance distance of unicyclic graphs

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## Degree Resistance Distance of Unicyclic Graphs

Let G be a connected graph with vertex set V (G). The degree resistance distance of G is defined as DR(G) = ∑ fu,vg V (G)[d(u) +d(v)]R(u, v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between u and v. In this paper, we characterize n-vertex unicyclic graphs having minimum and second minimum degree resistance distance.

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## Unicyclic and bicyclic graphs having minimum degree distance

In this paper characterizations of connected unicyclic and bicyclic graphs in terms of the degree sequence, as well as the graphs in these classes minimal with respect to the degree distance are given. © 2007 Elsevier B.V. All rights reserved.

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عنوان ژورنال:

دوره 39  شماره 4

صفحات  681- 706

تاریخ انتشار 2013-09-01

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