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Article: The study of [sigma]--index on Q([S.sub.k], [C.sub.s1], [C.sub.s2], ..., [C.sub.sk]) graphs.(Report)
- Article from:
- Scientia Magna
- Article date:
- June 1, 2008
- Author:
CopyrightCOPYRIGHT 2008 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract A Q([S.sub.k], [C.sub.s1], [C.sub.s2], ... , [C.sub.sk]) graphs be a graph abtained from [S.sub.k] whose every one degree vertex attached one cycle [C.sub.i](i = 1, 2, ... , k). In this paper, we determine the lower and the higher bound for the Merrifield--simmons index in Q([S.sub.k], [C.sub.s1], [C.sub.s2], ... , [C.sub.sk]) graphs in terms of the order k, and characterize the Q([S.sub.k], [C.sub.s1], [C.sub.s2], ... , [C.sub.sk]) graphs with the smallest and the largest Merrifield-simmons index.
Keywords Q([S.sub.k], [C.sub.s1], [C.sub.s2], ... , [C.sub.sk]) graphs, [sigma]-index or Merrifield--Simmons index.
[section] 1. Introduction