13 research outputs found
The extremal unicyclic graphs of the revised edge Szeged index with given diameter
Let be a connected graph. The revised edge Szeged index of is defined
as , where
(resp., ) is the number of edges whose distance to
vertex (resp., ) is smaller than the distance to vertex (resp.,
), and is the number of edges equidistant from both ends of
, respectively. In this paper, the graphs with minimum revised edge Szeged
index among all the unicyclic graphs with given diameter are characterized.Comment: arXiv admin note: text overlap with arXiv:1805.0657
The extremal unicyclic graphs with given diameter and minimum edge revised Szeged index
Let be a connected graph. The edge revised Szeged index of is defined as , where (resp., ) is the number of edges whose distance to vertex (resp., ) is smaller than to vertex (resp., ), and is the number of edges equidistant from and . In this paper, the extremal unicyclic graphs with given diameter and minimum edge revised Szeged index are characterized
Symmetry in Graph Theory
This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view