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First Year Mathematics Paper — I Algebra and Graph Theory Algebra: Unit1: Cartesian product of two sets, Functions or mappings, binary operations, Relations, Equivalence relations, Equivalence classes, partitions, Unit 2: Binary operation on a set Algebraic structure, Definition of group, finite and infinite groups, order of a finite group, General properties of groups, Definitions of a group based upon left axioms compositions tables for finite sets, Addition modulo m, Multiplication modulo p, Residue classes of the set of integers, An alternative set of postulates for a group, Unit 3: Permutations, group of permutations, cyclic permutations, Even and odd permutations. Integral powers of an element of a group order of an element of a group, Isomorphism of groups. Graph Theory : Unit V : Definition of graph, applications of graphs, incidence and degree, isolated vertex, pendant vertex and null graph, isomorphism, subgraphs, walks, paths and circuits, connected graphs, components Euler graphs, Hamiltonian paths and circuits, Incidence matrix and adjacency matrix. Vasishtha ,Krishna Prakashan Median p Ltd. New Delhi 2 C. Bhattachary, S. Jain, S.
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