Wai Chee Shiu

THE SPECTRUM OF THE EDGE CORONA OF TWO GRAPHS

Given two graphs G1, with vertices 1, 2, ..., n and edges e1, e2, ..., em, and G2, the edge corona G1 | G2 of G1 and G2 is defined as the graph obtained by taking m copies of G2 and for each edge ek = ij of G, joining edges between the two end-vertices i, j of ek and each vertex of the k-copy of G2. In this paper, the adjacency spectrum and Laplacian spectrum of G1 | G2 are given in terms of the spectrum and Laplacian spectrum of G1 and G2, respectively. As an application of these results, the number of spanning trees of the edge corona is also considered.

Forcing matching numbers of fullerene graphs

The forcing number or the degree of freedom of a perfect matching M of a graph G is the cardinality of the smallest subset of M that is contained in no other perfect matchings of G. In this paper we show that the forcing numbers of perfect matchings in a fullerene graph are not less than 3 by applying the 2-extendability and cyclic edge-connectivity 5 of fullerene graphs obtained recently, and Kotzigs classical result about unique perfect matching as well. This lower bound can be achieved by infinitely many fullerene graphs.

Resonance Graphs and a Binary Coding for the 1-Factors of Benzenoid Systems

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems

On independent domination number of regular graphs

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Orthogonal (g, f)-factorizations in networks

, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavzar et al.s result. The

On incidence coloring for some cubic graphs

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Normal components, Kekulé patterns, and Clar patterns in plane bipartite graphs

-dimensional vectors of nonnegative integers as a labelling for the 1-factors of

The 3-choosability of plane graphs of girth 4

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On Structure of Some Plane Graphs with Application to Choosability

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The strong chromatic index of complete cubic Halin graphs

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