By T.S. Bhanumurthy

Appropriate for college students and lecturers of arithmetic, this publication offers with the ancient continuity of Indian arithmetic, ranging from the Sulba Sutras of the Vedas as much as the seventeenth century.

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This c o r o l l a r y is a very special case of the result that cycles and cocycles of a graph over a field N(G) F are disjoint if and only if is not a m u l t i p l e of the c h a r a c t e r i s t i c of 4. F. See [6]). AN APPLICATION The graph shown in Figure 8 has a curious property. have been labelled L and R in such a way that if someone walks on its edges and always turns leftmost on a p p r o a c h i n g an always turns r i g h t m o s t on a p p r o a c h i n g an R-vertex, been t r a v e r s e d twice, and in opposite directions, to repeat.

Q(GA,X) theorem hypothesis positive integer the n u m b e r vertex, is thus that q, with the a P(G,I) sign of edges is l, of G. and satisfied. the theorem and c o n s i d e r is true the case whenever ~ = q.

One of Figure 11 graph. corresponds a variety H G). is a path obtained as indicated of this to l e f t - r i g h t path of yields H the next 9 shows (In [5] between that every plane entered graph of a single are ends that can be so o b t a i n e d the three a v a i l a b l e a left-right H (and it is easy to obtain if one has observation eulerian trees. to two such regions A component of a 4-regular so that if GRAPHS belonging is an extensive suitable of as described above, has a spanning connected partitions one vertex and vertices a graph there connected as follows: bicoloured; colour, labelling, that has an odd number of spanning RELATIONS G(H) G° 8 paths exactly of curious is the o b s e r v a t i o n to a c o m p o n e n t consequences.