Coin-Graph Recognition in Complete Trees

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# Coin-Graph Recognition in Complete Trees - PowerPoint PPT Presentation

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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Presentation Transcript
Coin-Graph Recognition in Complete Trees
• Amit Kumar Dey
• AftabHussain
• AnnajiatAlimRasel
• DipankarChaki Joy
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 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
• 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)