For a given graph G of order n, an L(2, 1)-labelling is defined as a function f : V (G) → {0, 1, 2, · · ·} such that |f(u)− f(v)| ≥ 2 when dG(u, v) = 1 and |f(u)− f(v)| ≥ 1 when dG(u, v) = 2, is the minimum length of a path between u and v. A k−L(2, 1)-labelling is an L(2, 1)-labelling such that no label is greater than k. The L(2, 1)-labelling number of G, denoted by λ(G), is the smallest numb...

A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce a new construction of supermagic graphs using the special structure of their subgraphs. The supermagic complements of some bipartite grap...

By strengthening an edge-decomposition technique for gracefully labelling a generalised Petersen graph, we provide graceful labellings for a new infinite family of such graphs. The method seems flexible enough to provide graceful labellings for many other classes of graphs in the future.

In this paper the author used graph theory and combinatorial analysis for enumeration of graphs of kinematic chains. Contracted graphs with up to four loops and six vertices are provided in Table 4. Based on the concept of expansion from contracted graphs, conventional graphs are generated. Conventional graphs with up to three independent loops and eight vertices are tabulated in Tables 5,6,7, ...

A graph is called supermagic if it admits a labelling of the edges by pairwise different consecutive positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. Some constructions of supermagic labellings of regular graphs are described. Supermagic regular complete multipartite graphs and supermagic cubes are characterized.

In this paper, we give infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [−1− √ 2,−2) and also infinitely many examples of (non-isomorphic) connected k-regular graphs with smallest eigenvalue in half open interval [α1,−1− √ 2) where α1 is the smallest root(≈ −2.4812) of the polynomial x3 + 2x2 − 2x − 2. From these results, we ...

iv Acknowledgements v List of Tables vii List of Graphs vii

the energy of a graph is equal to the sum of the absolute values of its eigenvalues. two graphs of the same order are said to be equienergetic if their energies are equal. we point out the following two open problems for equienergetic graphs. (1) although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pa...

We extend the de nition of edge-cordial graphs due to Ng and Lee for graphs on 4k, 4k+1, and 4k+3 vertices to include graphs on 4k+2 vertices, and show that, in fact, all graphs without isolated vertices are edge-cordial. Ng and Lee conjectured that all trees on 4k, 4k + 1, or 4k + 3 vertices are edge-cordial. Intuitively speaking, a graph G is said to be edge-cordial if its edges can be labell...

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