Some new classes of graceful diameter six trees

Here we denote a diameter six tree by (a0; a1, a2; . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr), where a0 is the center of the tree; ai; i = 1, 2, . . . ,m, bj , j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to a0; each ai is the center of a diameter f...

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Published in:TWMS journal of applied and engineering mathematics 2015-07, Vol.5 (2), p.269-269
Main Authors: Panda, Amaresh Chandra, Mishra, Debdas
Format: Article
Language:English
Subjects:
Analysis
Integer programming
Labels
Marking
Mathematical analysis
Proof theory
Theorems
Trees
Trees (Graph theory)
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Mishra, Debdas
description Here we denote a diameter six tree by (a0; a1, a2; . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr), where a0 is the center of the tree; ai; i = 1, 2, . . . ,m, bj , j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to a0; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pen-dant vertex. Here we give graceful labelings to some new classes of diameter six trees (a0; a1, a2, . . . , am; b1, b2, . . . ; bn; c1, c2, . . . , cr) in which the branches of a diameter four tree incident on a0 are of same type, i.e. either they are all odd branches or even branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree and an even branch if its center has an even degree.
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subjects Analysis
Integer programming
Labels
Marking
Mathematical analysis
Proof theory
Theorems
Trees
Trees (Graph theory)
title Some new classes of graceful diameter six trees
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