A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

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A Dynamic Survey of Graph Labeling

Distance-Regular Graphs

Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

An Introduction to the Theory of Graph Spectra: Spectral techniques

an introduction to the theory of graph spectra is available in our book collection an online access to it is set as public so you can download it instantly. Our digital library hosts in multiple countries, allowing you to get the most less latency time to download any of our books like this one. Merely said, the an introduction to the theory of graph spectra is universally compatible with any devices to read.

An Introduction To The Theory Of Graph Spectra

This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.

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Power graphs: A survey

The power graph of a finite group G is the graph whose vertices are the elements of G and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper, we study Laplacian spectrum of the power graph of additive cyclic group and the dihedral group . We show that the Laplacian spectrum of is the union of that of and . We find algebraic connectivity of and give bounds of the same for .

On Laplacian spectrum of power graphs of finite cyclic and dihedral groups

On the distance spectrum of distance regular graphs

A lower bound for radio k -chromatic number

A radio coloring of a simple connected graph G is a mapping f : V (G) → {0, 1, 2, . . .} such that |f(u)− f(v)| diam(G)+1−d(u, v) for each pair of distinct vertices u and v of G, where diam(G) is the diameter of G and d(u, v) is the distance between u and v in G. The span of a radio coloring f , span(f), is the number maxu∈V (G) f(u). The radio number of G, rn(G), is defined as minf{span(f) : f is a radio coloring of G}. In this paper, we determine the radio number of the toroidal grid Tm,n (the cartesian product of cycle Cm with the cycle Cn), when at least one of m and n is an even integer. Furthermore, a lower bound is given for the same when both m and n are odd integers.

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On the radio number of toroidal grids.

For any simple connected graph G with diameter d and an integer k, [email protected][email protected]?d, a radiok-coloring is an assignment f of positive integers to the vertices of G such that |f(u)-f(v)|>=1+k-d(u,v), where u and v are any two distinct vertices of G and d(u,v) is the distance between u and v. The maximum color (positive integer) assigned by f to some vertex of G is called the span of f. The minimum of spans of all possible radio k-colorings of G is called the radiok-chromatic number of G, denoted by rc"k(G). For k=d, the coloring is called the radio coloring and the radio d-chromatic number is the radio number of G. Kchikech et al. (2008) [3] have given upper and lower bounds for the radio k-chromatic number of the hypercube Q"n for n>=2. In this paper, we give an improved lower bound and prove that the bound is sharp for radio coloring.

Pratima Panigrahi

Papers

On Laplacian spectrum of power graphs of finite cyclic and dihedral groups

On the distance spectrum of distance regular graphs

A lower bound for radio k -chromatic number

On the radio number of toroidal grids.

An improved lower bound for the radio k-chromatic number of the hypercube Qn