48 research outputs found
General degree distance of graphs
We generalize several topological indices and introduce the general degree distance of a connected graph . For , the general degree distance , where is the vertex set of , is the degree of a vertex , and is the distance between and in . We present some sharp bounds on the general degree distance for multipartite graphs and trees of given order, graphs of given order and chromatic number, graphs of given order and vertex connectivity, and graphs of given order and number of pendant vertices
The Zagreb indices of graphs with a given clique number
AbstractFor a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Let Wn,k be the set of connected n-vertex graphs with clique number k. In this work we characterize the graphs from Wn,k with extremal (maximal and minimal) Zagreb indices, and determine the values of corresponding indices
A Survey on Monochromatic Connections of Graphs
The concept of monochromatic connection of graphs was introduced by Caro and
Yuster in 2011. Recently, a lot of results have been published about it. In
this survey, we attempt to bring together all the results that dealt with it.
We begin with an introduction, and then classify the results into the following
categories: monochromatic connection coloring of edge-version, monochromatic
connection coloring of vertex-version, monochromatic index, monochromatic
connection coloring of total-version.Comment: 26 pages, 3 figure