PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 44(58), pp. 2934 (1988) 

ON CONNECTED GRAPHS WITH MAXIMAL INDEXD. Cvetkovi\'c and P. RowlinsonElektrotehnicki fakultet, Beograd, Yugoslavia and Department of Mathematics, University of Stirling, Scotland FK94LAAbstract: Let ${\Cal H}(n,n+k)$ denote the set of all connected graps having $n$ vertices and $n+k$ edges ($k\geq 0$). The graphs in ${\Cal H}(n,n+k)$ with maximal index are determined (i) for certain small values of $n$ and $k$, (ii) for arbitrary fixed $k$ and large enough $n$. The results include a proof of a conjecture of Brualdi and Solheid [1]. Classification (MSC2000): 05C50 Full text of the article:
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