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A graph G is called chromatic-choosable if its choice number is equal to its chromatic number, namely Ch(G) = χ(G). Ohba has conjectured that every graph G satisfying |V (G)| ≤ 2χ(G)+1 is chromatic-choosable. Since each k-chromatic graph is a subgraph of a complete k-partite graph, we see that Ohba's conjecture is true if and only if it is true for every… (More)

A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetkovi´c and Lepovi´c, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetkovi´c and M. Lepovi´c. Cospectral graphs with least eigenvalue at least −2. Employing… (More)

Note The integral sum number of complete bipartite graphs K r; s Abstract A graph G =(V; E) is said to be an integral sum graph (sum graph) if its vertices can be given a labeling with distinct integers (positive integers), so that uv ∈ E if and only if u + v ∈ V. The integral sum number (sum number) of a given graph G, denoted by (G) ((G)), was deÿned as… (More)