3 research outputs found
Chromatic roots and limits of dense graphs
In this short note we observe that recent results of Abert and Hubai and of
Csikvari and Frenkel about Benjamini--Schramm continuity of the holomorphic
moments of the roots of the chromatic polynomial extend to the theory of dense
graph sequences. We offer a number of problems and conjectures motivated by
this observation.Comment: 9 page
Two Classes of Topological Indices of Phenylene Molecule Graphs
A phenylene is a conjugated hydrocarbons molecule composed of six- and four-membered rings. The matching energy of a graph G is equal to the sum of the absolute values of the zeros of the matching polynomial of G, while the Hosoya index is defined as the total number of the independent edge sets of G. In this paper, we determine the extremal graph with respect to the matching energy and Hosoya index for all phenylene chains