the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

the geometric-arithmetic index is another topological index was defined as2 deg ( )deg ( )( )deg ( ) deg ( )g guv eg gu vga gu v  , in which degree of vertex u denoted by degg (u). wenow define a new version of ga index as 4( )2 ε ( )ε ( )( )ε ( ) ε ( )g ge uv e g g gu vga g  u v , where εg(u) isthe eccentricity of vertex u. in this paper we compute this new topological index for twogr...

Waqas Nazeer 1, Shin Min Kang 2,3, Saima Nazeer 4, Mobeen Munir 1, Imrana Kousar 4, Ammara Sehar 4 and Young Chel Kwun 5,* 1 Division of Science and Technology, University of Education, Lahore 54000, Pakistan; [email protected] (W.N.); [email protected] (M.M.) 2 Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea; smkang@gn...

Five image processing algorithms are proposed to measure the average orientation, eccentricity and size of cells in images of biological tissue. These properties, which can be embodied by an elliptical ‘composite cell’, are crucial for biomechanical tissue models. To automatically determine these properties is challenging due to the diverse nature of the image data, with tremendous and unpredic...

A proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $G$ such that each vertex receives a color from its own list. In this paper, we prov...

A graph is a block if its blocks are all cliques. In this paper, we study the average eccentricity of graphs from perspective order sequences. An equivalence relation established under sequence and used to prove lower upper bounds on graphs. The result that 1 1n?34n2?12n?, respectively, where n graph. Finally, devise linear time algorithm calculate sequence.

We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues. In particular we prove the following results. Let G be a graph of order n, average degree d, independence number α (G) , and clique number ω (G) . (i) If μn is the smallest eigenvalue of G, then ω (G) ≥ 1 + dn (n− d) (d− μn) . Equality holds if and only if G is a complete regular ω-partite gr...