computing szeged index of graphs on ‎triples

Authors

m. r. darafsheh

school of mathematics, college of science, university of tehran r. modabernia

department of mathematics, shahid chamran university of ahvaz m. namdari

department of mathematics, shahid chamran university of ahvaz

abstract

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎‎types ‎of ‎intersection ‎graphs ‎with ‎vertex ‎set v. these graphs are denoted by ‎‎ ‎‎ and we will find their ‎szeged ‎indices.‎

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Computing Szeged index of graphs on ‎triples

ABSTRACT Let ‎G=(V,E) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎V‎‎‎ ‎and ‎edge ‎set ‎‎‎E. ‎The Szeged index ‎of ‎‎G is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎G ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎If ‎‎‎‎S ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎V ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎S ‎of ‎size ‎3. ‎Then ‎we ‎define ‎t...

full text

On the revised edge-Szeged index of graphs

The revised edge-Szeged index of a connected graph $G$ is defined as Sze*(G)=∑e=uv∊E(G)( (mu(e|G)+(m0(e|G)/2)(mv(e|G)+(m0(e|G)/2) ), where mu(e|G), mv(e|G) and m0(e|G) are, respectively, the number of edges of G lying closer to vertex u than to vertex v, the number of ed...

full text

Weighted Szeged Index of Graphs

The weighted Szeged index of a connected graph G is defined as Szw(G) = ∑ e=uv∈E(G) ( dG(u) + dG(v) ) nu (e)n G v (e), where n G u (e) is the number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. In this paper, we have obtained the weighted Szeged index Szw(G) of the splice graph S(G1, G2, y, z) and link graph L(G1, G2, y, z).

full text

Computing the Szeged index of 4,4 ׳-bipyridinium dendrimer

Let e be an edge of a G connecting the vertices u and v. Define two sets N1 (e | G) and N2(e |G) as N1(e | G)= {xV(G) d(x,u) d(x,v)} and N2(e | G)= {xV(G) d(x,v) d(x,u) }.The number of elements of N1(e | G) and N2(e | G) are denoted by n1(e | G) and n2(e | G) , respectively. The Szeged index of the graph G is defined as Sz(G) ( ) ( ) 1 2 n e G n e G e E    . In this paper we compute th...

full text

Revised Szeged Index of Product Graphs

The Szeged index of a graph G is defined as S z(G) = ∑ uv = e ∈ E(G) nu(e)nv(e), where nu(e) is number of vertices of G whose distance to the vertex u is less than the distance to the vertex v in G. Similarly, the revised Szeged index of G is defined as S z∗(G) = ∑ uv = e ∈ E(G) ( nu(e) + nG(e) 2 ) ( nv(e) + nG(e) 2 ) , where nG(e) is the number of equidistant vertices of e in G. In this paper,...

full text

Edge Szeged Index of Unicyclic Graphs

The edge Szeged index of a connected graph G is defined as the sum of products mu(e|G)mv(e|G) over all edges e = uv of G, where mu(e|G) is the number of edges whose distance to vertex u is smaller than the distance to vertex v, and mv(e|G) is the number of edges whose distance to vertex v is smaller than the distance to vertex u. In this paper, we determine the n-vertex unicyclic graphs with th...

full text

My Resources

Save resource for easier access later


Journal title:
iranian journal of mathematical chemistry

جلد ۸، شماره ۲، صفحات ۱۷۵-۱۸۰

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023