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Optimal trees for
functions of internal distance
Alex Collins, Fedelis Mutiso and Hua Wang
Vol. 5 (2012), No. 3, 371–378
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Abstract |
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The sum of distances between vertices of a tree has been considered from many aspects. The question of characterizing the extremal trees that maximize or minimize various such “distance-based” graph invariants has been extensively studied. Such invariants include, to name a few, the sum of distances between all pairs of vertices and the sum of distances between all pairs of leaves. With respect to the distances between internal vertices, we provide analogous results that characterize the extremal trees that minimize the value of any nonnegative and nondecreasing function of internal distances among trees with various constraints. |
Keywords
internal distances, trees, extremal
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Mathematical Subject Classification 2010
Primary: 05C05, 05C12
Secondary: 05C30
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Milestones
Received: 5 November 2012
Revised: 10 March 2013
Accepted: 30 March 2013
Published: 14 April 2013
Communicated by Jerrold Griggs
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Authors |
| Alex Collins | |
| Department of Mathematics and
Statistics Georgia State University Atlanta, GA 30303 United States |
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| Fedelis Mutiso | |
| Department of Mathematical
Sciences Georgia Southern University Statesboro, GA 30460 United States |
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| Hua Wang | |
| Department of Mathematical
Sciences Georgia Southern University Statesboro, GA 30460 United States |
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