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A graph G is said to be chromatic-choosable if ch(G)= (G). Ohba has conjectured that every graph G with 2 (G)+ 1 or fewer vertices is chromatic-choosable. It is clear that Ohba’s conjecture is true if and only if it is true for complete multipartite graphs. But for complete multipartite graphs, the graphs for which Ohba’s conjecture has been verified are(More)
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)
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)
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)