Yong-Zhi Kan
Abstract
Let G be a simple graph,for G1■G,let d(G1) = ∑v ∈ V(G)d(v),where d(v) is degree of the vertices v.The main result is as Follows: Let G be a simple connected,almost brideless graph of order n ≥ 3,G = K1,n-1,Q1 and Q2,if d(I) ≥ 2n-6 for each induced subgraph I isomorphic to 4 vertex road,then line graph L(G) of G has Hamiltonian cycles.
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Let G be a simple graph,for G1■G,let d(G1) = ∑v ∈ V(G)d(v),where d(v) is degree of the vertices v.The main result is as Follows: Let G be a simple connected,almost brideless graph of order n ≥ 3,G = K1,n-1,Q1 and Q2,if d(I) ≥ 2n-6 for each induced subgraph I isomorphic to 4 vertex road,then line graph L(G) of G has Hamiltonian cycles.
Key concepts: Mathematics, Combinatorics, Graph, Simple graph, Hamiltonian path, Vertex (graph theory), Line graph, Bound graph