Displaying similar documents to “Cospectral Graphs With Least Eigenvalue at Least -2”

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

Similarity:

For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

The inertia of unicyclic graphs and bicyclic graphs

Ying Liu (2013)

Discussiones Mathematicae - General Algebra and Applications

Similarity:

Let G be a graph with n vertices and ν(G) be the matching number of G. The inertia of a graph G, In(G) = (n₊,n₋,n₀) is an integer triple specifying the numbers of positive, negative and zero eigenvalues of the adjacency matrix A(G), respectively. Let η(G) = n₀ denote the nullity of G (the multiplicity of the eigenvalue zero of G). It is well known that if G is a tree, then η(G) = n - 2ν(G). Guo et al. [Ji-Ming Guo, Weigen Yan and Yeong-Nan Yeh. On the nullity and the matching number...

Note on enumeration of labeled split graphs

Vladislav Bína, Jiří Přibil (2015)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The paper brings explicit formula for enumeration of vertex-labeled split graphs with given number of vertices. The authors derive this formula combinatorially using an auxiliary assertion concerning number of split graphs with given clique number. In conclusion authors discuss enumeration of vertex-labeled bipartite graphs, i.e., a graphical class defined in a similar manner to the class of split graphs.