The Gutman index and the edge-Wiener index of graphs with given vertex-connectivity
نویسندگان
چکیده
منابع مشابه
On the Wiener Index of Some Edge Deleted Graphs
The sum of distances between all the pairs of vertices in a connected graph is known as the {it Wiener index} of the graph. In this paper, we obtain the Wiener index of edge complements of stars, complete subgraphs and cycles in $K_n$.
متن کاملTotal Szeged Index, Vertex-Edge Wiener Index and Edge Hyper-Wiener Index of Certain Special Molecular Graphs
In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...
متن کاملThe augmented Zagreb index, vertex connectivity and matching number of graphs
Let $Gamma_{n,kappa}$ be the class of all graphs with $ngeq3$ vertices and $kappageq2$ vertex connectivity. Denote by $Upsilon_{n,beta}$ the family of all connected graphs with $ngeq4$ vertices and matching number $beta$ where $2leqbetaleqlfloorfrac{n}{2}rfloor$. In the classes of graphs $Gamma_{n,kappa}$ and $Upsilon_{n,beta}$, the elements having maximum augmented Zagreb index are determined.
متن کاملMORE ON EDGE HYPER WIENER INDEX OF GRAPHS
Let G=(V(G),E(G)) be a simple connected graph with vertex set V(G) and edge set E(G). The (first) edge-hyper Wiener index of the graph G is defined as: $$WW_{e}(G)=sum_{{f,g}subseteq E(G)}(d_{e}(f,g|G)+d_{e}^{2}(f,g|G))=frac{1}{2}sum_{fin E(G)}(d_{e}(f|G)+d^{2}_{e}(f|G)),$$ where de(f,g|G) denotes the distance between the edges f=xy and g=uv in E(G) and de(f|G)=∑g€(G)de(f,g|G). In thi...
متن کاملRelationship between Edge-wiener Index and Gutman Index of a Graph
The Wiener indexW (G) of a connected graphG is defined to be the sum ∑ u,v d(u, v) of the distances between the pairs of vertices in G. Similarly, the edge-Wiener index We(G) of G is defined to be the sum ∑ e,f d(e, f) of the distances between the pairs of edges in G, or equivalently, the Wiener index of the line graph L(G). Finally, the Gutman index Gut(G) is defined to be the sum ∑ u,v deg(u)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2016
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1900