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


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


  • 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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