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Coin-Graph Recognition in Complete Trees

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

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  1. Coin-Graph Recognition in Complete Trees • Amit Kumar Dey • AftabHussain • AnnajiatAlimRasel • DipankarChaki Joy

  2. Considering Trees

  3. 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

  4. Tree arity Vs space required for leaf nodes Tree Height • combined diameter of leaf nodes

  5. Tree arity Vs space required for leaf nodes Tree Height • 100 base log of combined diameter of leaf nodes

  6. 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

  7. 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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