Regular graphs with excess one

Abstract It is shown that there exists no regular graph with excess e =1 and girth 2 r +1⩾5.

[1]  Norman Biggs,et al.  Graphs with even girth and small excess , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  Norman Biggs,et al.  Girth, valency, and excess , 1980 .

[3]  W. G. Brown.  On the Non-Existence of a Type of Regular Graphs of Girth 5 , 1967, Canadian Journal of Mathematics.

[4]  E. Bannai,et al.  On finite Moore graphs , 1973 .

[5]  J. A.,et al.  On Moore Graphs with Diameters 2 and 3 , 2022 .

[6]  N. Biggs.  Algebraic Graph Theory: COLOURING PROBLEMS , 1974 .

[7]  R. M. Damerell.  On Moore graphs , 1973, Mathematical Proceedings of the Cambridge Philosophical Society.