Geodesic
On Eulerian and Hamiltonian Graphs and Line Graphs
Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 701-709

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A graph G has a finite set V of points and a set X of lines each of which joins two distinct points (called its end-points), and no two lines join the same pair of points. A graph with one point and no line is trivial. A line is incident with each of its end-points. Two points are adjacent if they are joined by a line. The degree of a point is the number of lines incident with it. The line-graph L(G) of G has X as its set of points and two elements x, y of X are adjacent in L(G) whenever the lines x and y of G have a common end-point. A walk in G is an alternating sequence v1, x1, v2, x2, ..., vn of points and lines, the first and last terms being points, such that xi is the line joining vi to vi+1 for i=1, ..., n-1. 
Harary, Frank; Nash-Williams, C. St. J. A. On Eulerian and Hamiltonian Graphs and Line Graphs. Canadian mathematical bulletin, Tome 8 (1965) no. 6, pp. 701-709. doi: 10.4153/CMB-1965-051-3
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