A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...

The general sum-connectivity index of a graph $G$ is defined as $chi_{alpha}(G)= sum_{uvin E(G)} (d_u + d_{v})^{alpha}$ where $d_{u}$ is degree of the vertex $uin V(G)$, $alpha$ is a real number different from $0$ and $uv$ is the edge connecting the vertices $u,v$. In this note, the problem of characterizing the graphs having extremum $chi_{alpha}$ values from a certain collection of polyomino ...

We consider vertex colorings of graphs in which each color has an associated cost which is incurred each time the color is assigned to a vertex. The cost of the coloring is the sum of the costs incurred at each vertex. The cost chromatic number of a graph with respect to a cost set is the minimum number of colors necessary to produce a minimum cost coloring of the graph. We show that the cost c...

21 Corollary 5.4 If the execution time of any job is then a schedule which approximates the minimal average response time within a factor of +2 3 can be found distributively in O(log 2 n) communication rounds. For the subclass of connict graphs for which a maximum independent set can be found in polynomial time, the minimum average response time can be approximated to within a factor of 4 using...

An edge labeling of a connected graph $G = (V, E)$ is said to be local antimagic if it bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex label $f^+(x)= \sum f(e)$, with $e$ ranging over all edges incident $x$. The chromatic number $G$, denoted by $\chi_{la}(G)$, minimum distinct labels labelings $G$. In this...

We present a detailed motivation for the notions of the chromatic derivatives and the chromatic expansions. The chromatic derivatives are special, numerically robust linear differential operators. The chromatic expansions are the associated local expansions, which possess features of both the Taylor and the Nyquist expansions. We give simplified treatment of some of the basic properties of the ...

In this paper we present an one-and-a-half-line proof, involving Cogalois Theory, of a folklore result asking when is an irrational number a sum of radicals of positive rational numbers. Some of the main ingredients of Cogalois Theory like G-Kneser extension, G-Cogalois extension, etc., used in the proof are briefly explained, so that the paper is selfcontained. We also discuss some older and n...

A generalization of the Davenport constant is investigated. For a finite abelian group G and a positive integer k, let D k (G) denote the smallest ℓ such that each sequence over G of length at least ℓ has k disjoint non-empty zero-sum subsequences. For general G, expanding on known results, upper and lower bounds on these invariants are investigated and it is proved that the sequence (D k (G)) ...

A (p,q) graph G is said to admit n order triangular sum labeling if its vertices can be labeled by non negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q n order triangular numbers. A graph G which admits n order triangular sum labeling is called n order triangular sum graph. In this paper we prove that paths, combs, stars, subd...