On the edge -to -vertex detour number of a graph
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For two vertices u and v in a graph G=(V,E), The detour distance D(u,v) s the length of a longest, u-v path in G. A u-v path of length D(u,v) is called a u-v detour. For subsets A and B of V, the detour distance D(A,B) is defined as D(A,B)=(formula). A u-v path of length D(A,B) is called an A-B detour joining the sets A, B⊆V where u∈B. A vertex x is said to lie on an A-B detour is a vertex of A-B detour. A set S⊆E is called an detour joining a pair of edges of S. The edge-to-vertex detour number dn2(G) OF G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn2(G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn2(G) = q or dn2(G) = q-1 or dn2(G) = q-2 are characterized.
Abstract
For two vertices u and v in a graph G=(V,E), The detour distance D(u,v) s the length of a longest, u-v path in G. A u-v path of length D(u,v) is called a u-v detour. For subsets A and B of V, the detour distance D(A,B) is defined as D(A,B)=(formula). A u-v path of length D(A,B) is called an A-B detour joining the sets A, B⊆V where u∈B. A vertex x is said to lie on an A-B detour is a vertex of A-B detour. A set S⊆E is called an detour joining a pair of edges of S. The edge-to-vertex detour number dn2(G) OF G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn2(G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn2(G) = q or dn2(G) = q-1 or dn2(G) = q-2 are characterized.
참고문헌 (9)
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