![]() ![]() ![]() Thus defining two notions concerning vertices which one of them is fuzzy(neutrosophic) titled twin and another is crisp titled antipodal to study the behaviors of cycles which are partitioned into even and odd, are concluded. Fuzzification (neutrosofication) of twin vertices but using crisp concept of antipodal vertices are another approaches of this study. complete, strong, t-partite, bipartite, star and wheel in the formation of individual case and in the case, they form a family are studied in the term of dimension. ![]() Fuzzy(neutrosophic) graphs, under conditions, fixed-edges, fixed-vertex and strong fixed-vertex are studied. Behaviors of twin and antipodal are explored in fuzzy(neutrosophic) graphs. New notion of dimension as set, as two optimal numbers including metric number, dimension number and as optimal set are introduced in individual framework and in formation of family. The fewer the pegs remaining at the end of the game, the higher the score. Pegs are removed when they are jumped by another peg into an empty space. By generalizing a result of Chan and Godbole, Postle showed that for a graph with diameter $d$, $\pi(G) \le n 2^$ is the graph on two vertices and $r$ parallel edges. Peg Solitaire (also known as Solo Noble or Brainvita) is a classic single player board game the objective of which is to clear all the pegs or marbles except one from the board. Clarke, Hochberg, and Hurlbert demonstrated that every connected undirected graph on $n$ vertices with diameter 2 has $\pi(G) = n$ unless it belongs to an exceptional family of graphs, consisting of those that can be constructed in a specific manner in which case $\pi(G) = n 1$. Previous work has related $\pi(G)$ to the diameter of $G$. use pebbling moves to have a pebble reach any predetermined vertex. The pebbling number, $\pi(G)$, is the minimum number of pebbles such that regardless of their exact configuration, the player can. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble reach a predetermined vertex. ![]()
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