In a connected graph G, between any pair of vertices, say x and y, the longest x −y path is the detour path, and its length is its detour distance D(x,y). A subset S of V(G) where every vertices of G lie on some detour path joining a pair of vertices in S. The minimum cardinality of such S is the detour number dn(G). A decomposition Π = (G1,G2,...,Gn) is said to be detour self-decomposition of G, if dn(G) = dn(Gi),1 ≤ i ≤ n. If any pair of subgraphs in Π is isomorphic to each other, such Π is called an isomorphic detour self-decomposition. If any pair of subgraphs in Π is non-isomorphic to each other, such Π is called a non isomorphic detour self- decompoition. Graphs satisfying these decompositions are studied here.
Author
(s) Details
Anlin
Bena. E
Department of Mathematics, Nesamony Memorial Christian College,
Marthandam, Tamil Nadu-629 165, Affiliated to Manonmaniam Sundaranar
University, Abishekapatti, Tirunelveli, Tamil Nadu-627012, India.
E. Ebin
Raja Merly
Department of Mathematics, Nesamony Memorial Christian College,
Marthandam, Tamil Nadu-629 165, India.
Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v10/3236
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