International Journal of Mathematics and Soft Computing

11-16

Authors: Rao Li

The Wiener index of a connected graph is defined as the sum of distances between all pairs of vertices in the graph. Yang presented a sufficient condition in terms of the Wiener index for a graph to be traceable. Motivated by Yang’s result, we present sufficient conditions based on the Wiener index for a graph to be Hamiltonian or Hamilton-connected in this note.

23-29

Authors: N Adalin Beatress, P. B Sarasija

A graph G(V, E) with n vertices and m edges is said to be even-odd harmonious if there exists an injection f : V(G) →{ 1, 3, 5,…, 2n-1} such that the induced mapping f *:E(G) → {0,2,4,…,2(m-1)} defined by f*(uv) = [f(u) + f(v)] (mod 2m) is a bijection. The function f is called even-odd harmonious labeling of G. In this paper, we prove that the bistar graph Bm,n, cycle with one pendent edge, crown graph, the graph K1,m,n. the prism graph C3Yn and the graph nP2 are even-odd harmonious graphs.

45-55

Authors: Keerthipati Kumar, K Narayana, B Sangmitra

The tremendous growth of the internet and the advances of computer technology have been pushing forward computer networks for high speed and broad bandwidth. Congestion, being a non-linear and dynamic problem requires robust, possibly intelligent, control methodologies to obtain satisfactory performance. Fuzzy logic helps to increase throughput, reduction in packet drop and delays. In this paper, we illustrate the power of the methodology by the successful application of fuzzy based congestion control in the two diverse networking technologies of ATM and TCP/IP.

73-78

Authors: S M Karthikeyan, S Navanaeethakrishnan, R Sridevi

A total edge Fibonacci irregular labeling $f: V(G) \cup E(G) \rightarrow \{1,2,\dots,K\}$ of a graph $G=(V,E)$ is a labeling of vertices and edges of $G$ in such a way that for any different edges $xy$ and $x^{'}y^{'}$ their weights $f(x)+f(xy)+f(y)$ and $f(x^{'})+f(x^{'}y^{'})+f(y^{'})$ are distinct Fibonacci numbers. The total edge Fibonacci irregularity strength, tefs($G$) is defined as the minimum $K$ for which $G$ has a total edge Fibonacci irregular labeling. If a graph has a total edge Fibonacci irregular labeling, then it is called a total edge Fibonacci irregular graph. In this paper, we prove $K_{1,n}$, bistar $\textless(B_{n,n})\textgreater$, subdivision of bistar$\textless(B_{n,n};W)\textgreater$ and $\textless(B_{2,n};W_i)\textgreater$ $(1\leq i\leq n)$ are total edge Fibonacci irregular graphs.

93-103

Authors: S Saravanakumar, K Nagarajan

Let G = (V;E) be a (p; q) - graph. A shortest path P is called an odd path if l(P) is an odd positive integer. Odd distance graph OD(G) of a graph G is defined as the graph with vertex set V (G) and two vertices are adjacent if the distance between them is odd. In this paper, we deal with the odd distance graph of standard graphs such as path, cycle, star, wheel, complete graph, complete bipartite graph and corona of a complete graph etc. Also we give some properties and characterizations for odd distance graphs.

111-117

Authors: V J Kaneria, H M Makadia, Meera Meghapara

In this paper we present graceful labelings for $C(t\cdot P_{n}\times P_{m})$, $(P_{n}\times P_{m})^{\star}$ and path union of $t$ copies of the grid graph $P_{n}\times P_{m}$.

129-141

Authors: M V Modha, K K Kanani

In this paper, we discuss here 5-cordial labeling of some new graph families. We prove that prisms are 5-cordial. We also prove that web graph, flower graph and closed helm admit 5-cordial labeling.

155-164

Authors: G V Ghodasara, I I Jadav

A function from the vertex set of a graph G to the set f0,1,2g is called 3

171-186

Authors: Amara Jothi, J Baskar Babujee, N. G David

A labeling of a graph G of type assigns labels from the set to the vertices, edges and faces of G such that each vertex receives a label(s), each edge receives b label(s) and each face receives c label(s) and each number is used exactly once as a label. We restrict a, b and c to be not greater than one. The weight of face w(f) under a labeling is the sum of labels of the face itself together with labels of vertices and edges surrounding that face. A labeling is said to be magic, if for every positive integer s, all s-sided faces have the same weight. In this paper, we examine whether vertex and edge duplication on some families of graphs admit face magic labeling of types (1, 0, 1), (1, 1, 0), (0, 1, 1) and (1, 1, 1).