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A graph is cubic if each of its vertex is of degree 3 and it is hamiltonian if it contains a cycle passing through all its vertices. It is known that if a cubic graph is hamiltonian, then it has at least three Hamilton cycles. This paper is about those works done concerning the number of Hamilton cycles in cubic graphs and related problems. A graph is… (More)
In this paper, it is shown that the graph obtained by overlapping the cycle and the complete tripartite graph at an edge is uniquely determined by its chromatic polynomial.) 3 (≥ m C m 2 , 2 , 2 K Let G be a finite graph with neither loops nor multiple edges and let) ; (λ G P denote its chromatic polynomial. Then G is said to be chromatically unique if) ;… (More)
This paper investigates on those smallest regular graphs with given girths and having small crossing numbers.
We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph K m,n,r. Using these, we establish the chromatic equivalence classes for K 1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that K… (More)