1 / 10

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

rozene
Download Presentation

Coin-Graph Recognition in Complete Trees

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related