Topological indices of Sierpiński Gasket and Sierpiński Gasket Rhombus graphs

Sierpiński graphs S(n, k) were defined originally in 1997 by Sandi Klavžar and Uroš Milutinović. In this paper atom bond connectivity index, fourth atom bond connectivity indices, geometric arithmetic index, fifth geometric arithmetic indices, augmented Zagreb index and sankruti index of Sierpiński Gasket graphs and Sierpiński Gasket Rhombus graphs are determined.The first author is supported by University Grants Commission, Government of India, for the financial support under the Basic Science Research Fellowship.UGC vide No.F.25 − 1/2014 − 15(BSR)/7 − 349/2012(BSR), January 2015.The Second author is partially supported by the University Grants Commission for financial assistance under No.F.510/12/DRS-II/2018(SAP-I).Publisher's Versio

Hub-integrity of splitting graph and duplication of graph elements

The hub-integrity of a graph G = (V (G), E(G)) is denoted as HI(G) and defined by HI(G) = min{|S| + m(G − S), S is a hub set of G}, where m(G − S) is the order of a maximum component of G − S. In this paper, we discuss hub-integrity of splitting graph and duplication of an edge by vertex and duplication of vertex by an edge of some graphs.Publisher's Versio

Bharath hub number of graphs

The mathematical model of a real world problem is designed as Bharath hub number of graphs. In this paper, we study the graph theoretic properties of this variant. Also, we give results for Bharath hub number of join and corona of two connected graphs, cartesian product and lexicographic product of some standard graphs.Publisher's Versio

Domination Integrity of Line Splitting Graph and Central Graph of Path, Cycle and Star Graphs

The domination integrity of a connected graph G = (V (G);E(G)) is denoted as DI(G) and defined by DI(G) = min{|S| + m(G - S)}, where S is a dominating set and m(G-S) is the order of a maximum component of G-S. This paper discusses domination integrity of line splitting graph and central graph of some graphs

The Eccentric-distance Sum of Some Graphs

Let $G = (V,E)$ be a simple connected graph. Theeccentric-distance sum of $G$ is defined as\xi^{ds}(G) =\ds\sum_{\{u,v\}\subseteq V(G)} [e(u)+e(v)] d(u,v), where $e(u)$ %\dsis the eccentricity of the vertex $u$ in $G$ and $d(u,v)$ is thedistance between $u$ and $v$. In this paper, we establish formulaeto calculate the eccentric-distance sum for some graphs, namelywheel, star, broom, lollipop, double star, friendship, multi-stargraph and the join of $P_{n-2}$ and $P_2$

Amplified eccentric connectivity index of graphs

A new distance based graphical index, coined as amplified eccentric connectivity index, has been established and the formulae to calculate the amplified eccentric connectivity index of some standard graphs, Dutch windmill graph and molecular graph of cycloalkenes has been computed. Also, in the case of boiling points of primary and secondary amines, the study shows that the amplified eccentric connectivity index gives a greater correlation of 98%, when compared to the Wiener and Eccentric connectivity indices

Neighborhub number of graphs

Let G be a graph. A neighborhub set (n-hub set) S of G is a set of vertices with the property that for any pair of vertices outside of S, there is a path between them with all intermediate vertices in S and G = S Uv∈S . The neighborhub number (n-hub number) hn(G) is then defined to be the size of a smallest neighborhub set of G. In this paper, the neighborhub number for several classes of graphs is computed, bounds in terms of other graph parameters are also determined.Emerging Sources Citation Index (ESCI)MathScinetScopu

Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs

For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G). The equality symbol '=' stands for on isomorphism between two graphs

Miscellaneous Properties Of Full Graphs

In this paper, we stablish miscellaneous properties of the full graph of a graph. We obtain characterizations of this graph. Also, we prove that for any connected graph G, the full graph of G is not separable