Department of Mathematics, Velammal Engineering College, Chennai, India. We begin with the plane coloring problem. What is the least number of colors needed to color all the points of the Euclidean ...

This is a preview. Log in through your library . Abstract Let HG(x, y) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and φ(G) = ...

Abstract: The b-chromatic number of a graph, written as φ(G), is the highest number of colors you can use to color the graph properly, with one special rule: in each color group, there must be at ...

Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

Abstract: The homology of Kontsevich's commutative graph complex parametrizes finite type invariants of odd-dimensional manifolds. This graph homology is also the twisted homology of Outer Space ...

This is a preview. Log in through your library . Abstract We present a catalogue of the 236 (connected) bicyclic graphs on eight vertices. Eigenvalues, some spectral moments and the coefficients of ...

ABSTRACT: Let G be a graph and A=(aij)n×n be the adjacency matrix of G, the eigenvalues of A are said to be the eigenvalues of the graph G, and to form the spectrum of this graph. The numbers of ...