Let ej denote the number of vertices of eccentricity j in a graph. We provide sharp lower bounds on ej in graphs of given connectivity and in chordal graphs of given connectivity.

introduction: strength training has an important role in the exercise programs of normal individuals and athletes and it also has numerous benefits on the health of human body and spirit. one of the types of these exercise is eccentric resistance exercise which is associated with negative physiological changes. thus: this study examined the effects of a single bout of eccentric resistance exerc...

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.

The connective eccentric index of a graph is a topological index involving degrees and eccentricities of vertices of the graph. In this paper, we have studied the connective eccentric index for double graph and double cover. Also we give the connective eccentric index for some graph operations such as joins, symmetric difference, disjunction and splice of graphs. MSC (2010): Primary: 05C35; Sec...

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.

Four pendenticity based topological descriptors termed as superaugmented pendentic indices have been conceptualized in the present study. An in-house computer program was utilized to compute index values of all the possible structures (with at least one pendent vertex) containing four, five and six vertices. The sensitivity towards branching, discriminating power, degeneracy and mathematical pr...

In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound.