Bounds on Gutman Index
نویسندگان
چکیده
The Gutman index (also known as Schultz index of the second kind) of a graph G is defined as Gut(G) = ∑ u,v∈V (G) d(u)d(v)d(u, v). We show that among all graphs on n vertices, the star graph Sn has minimal Gutman index. In addition, we present upper and lower bounds on Gutman index for graphs with minimal and graphs with maximal Gutman index. Corresponding author Supported by project 1M0545 of the Czech Ministry of Education and by the CZ-SL bilateral project MEB 090805. Supported by the CZ-SL bilateral project MEB 090805. ~ Page 1 of 11 ~ Pr ep ri n t se ri es , I M FM , I S S N 2 23 220 94 , n o. 1 15 4, J u n e 23 , 2 01 1
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