coin graph recognition in complete trees
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Coin-Graph Recognition in Complete Trees. Amit Kumar Dey Aftab Hussain Annajiat Alim Rasel Dipankar Chaki Joy. Considering Trees. Fitting coins tree in a circle running over leaf nodes . 1 edge = 2r R = h x 2r Circumference =2 π R = 2 π (h x 2r) = 4 π rh

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coin graph recognition in complete trees
Coin-Graph Recognition in Complete Trees
  • Amit Kumar Dey
  • AftabHussain
  • AnnajiatAlimRasel
  • DipankarChaki Joy
fitting coins tree in a circle running over leaf nodes
Fitting coins tree in a circle running over leaf nodes
  • 1 edge = 2r
  • R = h x 2r
  • Circumference

=2πR

= 2π(h x 2r)

= 4 π rh

  • Number of nodes at leaf

= 2h

  • Total Diameter of nodes

=2h x 2r

= 2h+1 x r

r

r

r

r

r

r

tree arity vs space required for leaf nodes
Tree arity Vs space required for leaf nodes

Tree Height

  • combined diameter of leaf nodes
slide7

Tree arity Vs space required for leaf nodes

Tree Height

  • 100 base log of combined diameter of leaf nodes
research outcome
Research Outcome
  • Today’s findings:
    • Maximum height of tree
      • Binary tree: 5
      • Ternary tree: 2
      • Quarternary tree: 1
      • 5-ary tree: 1
    • 6-ary tree: 0 (It can be shown from the work done in 1st brainstorming workshop)
  • A complete tree is NOT a coin graph

(sufficient condition)

    • it is n-ary tree (n>=6)
    • Its height is longer than mentioned above
slide9

1st workshop Findings: Tree is not a coin graph if there exists any vertex with degree > 5

  • So, 6-ary tree is NOT possible
  • (becomes a wheel graph with a cycle)
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