Electronic Journal of Graph Theory and Applications, 2017
r are the vertices of the tree adjacent to c; each a i is the center of a diameter four tree, eac... more r are the vertices of the tree adjacent to c; each a i is the center of a diameter four tree, each b j is the center of a star, and each c k is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees (c; a 1 , a 2 ,. .. , a m ; b 1 , b 2 ,. .. , b n ; c 1 , c 2 ,. .. , c r) in which a diameter four tree may contain any combination of branches with the total number of branches odd though with some conditions on the number of odd, even, and pendant branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree, an even branch if its center has an even degree, and a pendant branch if it is a pendant vertex.
International Journal of Mathematics Trends and Technology, 2017
In this paper some new type of odd graceful graphs are investigated. We prove that the graph obta... more In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C 8 with some star graphs S 1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C 12 with some star graphs S 1,r keeping two, three and five vertices gap between pair of vertices of the cycle admits odd graceful labelling. We observed that C 8 ʘ S 4 1,r with one vertex gap, C 8 ʘ S 2 1,r three vertices gap between pair of vertices of the cycle C 8 are odd graceful , C 12 ʘ S 6 1,r with one vertex gap, C 12 ʘ S 4 1,r two vertices gap, C 12 ʘ S 3 1,r with three vertices gap and C 12 ʘ S 2 1,r with five vertices gap between pair of vertices are odd graceful graphs.
Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many ... more Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is introduced using color graphs to model all the 512 linear rules. The graph theoretic properties therefore studied in this paper simplifies the analysis of all linear rules in comparison with other ways of its study.
Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many ... more Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is introduced using color graphs to model all the 512 linear rules. The graph theoretic properties therefore studied in this paper simplifies the analysis of all linear
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Papers by Sushant Rout