Ordering connected graphs having small degree distances |
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Authors: | Ioan Tomescu |
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Affiliation: | Faculty of Mathematics and Computer Science, University of Bucharest, Str. Academiei, 14, 010014 Bucharest, Romania |
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Abstract: | The concept of degree distance of a connected graph G is a variation of the well-known Wiener index, in which the degrees of vertices are also involved. It is defined by D′(G)=∑x∈V(G)d(x)∑y∈V(G)d(x,y), where d(x) and d(x,y) are the degree of x and the distance between x and y, respectively. In this paper it is proved that connected graphs of order n≥4 having the smallest degree distances are K1,n−1,BS(n−3,1) and K1,n−1+e (in this order), where BS(n−3,1) denotes the bistar consisting of vertex disjoint stars K1,n−3 and K1,1 with central vertices joined by an edge. |
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Keywords: | Degree distance Eccentricity Diameter Tree Bistar |
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