# National Conference on Energy of Graphs

National Conference on Energy of Graphs Conference Papers "

On Spectral Radius of Graphs[ ]

Let G(V, E) be simple graph with n vertices and m edges and A be vetex subset of V(G ). For any v?A the degree of the vertex v_i with respect to the subset A is defined as the number of vertices A that are adjacent to v_i . We call it as D-degree and is denoted by D_i. Denote ?_1 (G) as the largest eigenvalue of the graph G and s_i.as the sum of ?? degree of vertices that are adjacent to v_i. In this paper we give lower bounds of ?_1 (G) in terms of ?? degree.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
The Maximum Eccentricity Energy of a Graph[ ]

In This paper, we introduce the concept of maximum eccentricity matrix of a connected graph and obtain some coefficients of the characteristic polynomial of the maximum eccentricity matrix of . We also introduce maximum eccentricity energy of a connected graph . Maximum eccentricity energies of some well-known graphs are obtained. Upper and lower bounds for are established. It is shown that if is a self-centred -regular graph with diameter , then is a maximum eccentricity eigenvalue of and . Moreover, it is also shown that if the maximum eccentricity energy of a graph is rational then it must be an even .

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
MINIMUM DOMINATING SEIDEL ENERGY OF A GRAPH[ ]

In This paper, we introduce the concept of minimum dominating seidel energy of a graph SED(G) and computed minimum dominating seidel energy of a star graph, complete graph crown graph and cocktail party graphs. Upper and lower bounds for SED(G)are established.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
A Note on Energy of Order Prime Graph of a Finite Group[ ]

The order prime graph OP(G) of a fnite group G is defined as a graph with the vertex set V(OP(G)) = G and two vertices a and b are adjacent in OP(G) if and only if (o(a),o(b))=1. The concept of order prime graph was introduced by M. Sattanathan and R. Kala (2009). The energy of a graph is the sum of the absolute values of the eigenvalues of the adjacency matrix of the graph. The concept of energy of a graph was introduced by I.Gutman (1978). In this paper, we discuss some results on eigenvalues and energy of order prime graphs of finite groups.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Degree Distance of Adjoin of Trees[ ]

For a graph G = (V, E) the degree distance of G is defined as where degG(u) is the degree of the vertex u in G and dG(u,v)is the shortest distance between u and v. In this paper we establish formulae to calculate the degree distance of adjoin of trees.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Topological Indices of Complete Graph with a Single rooted Vertex[ ]

A topological index of a chemical compound characterizes the compound and obeys a particular rule. In this paper, we find the Harmonic Index and the custom defined Redefined Zagreb Indices of Complete Graph with a single rooted vertex.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Some Bounds for Harary Index of Graphs[ ]

Harary index of graph is defined as the sum of reciprocal of distance between all pairs of vertices of the graph and is denoted by . Eccentricity of vertex in is the distance to a vertex farthest from . In this paper we obtain some bounds for in terms of eccentricities. Further we extend these results to the self-centered graphs and also we have given simple algorithm to find the Harary index of graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Narumi-Katayama and Multiplicative Zagreb Indices of Dutch Windmill Graph[ ]

In this paper, we compute Narumi - Katayama index, First multiplicative Zagreb index, Modified multiplicative Zagreb index of Dutch windmill graph.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Some Polygonal Sum Labeling of Bistar[ ]

A (p, q) graph G is said to admit a polygonal 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 polygonal numbers. A graph G which admits a polygonal sum labeling is called a polygonal sum graph. In this paper we have proved that the Bistar (Bn,n) admit Pentagonal, Hexagonal, Heptagonal, Octagonal, Nonagonal and Decagonal Sum Labeling.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
SUPER GEOMETRIC MEAN LABELING OF SOME UNION OF GRAPHS[ ]

Let G be a graph with p vertices and q edges. Let be a injective function. For a vertex labeling f, the induced edge labeling is defined by . Then f is called a Super Geometric mean labeling if . A graph which admits Super Geometric mean labeling is called Super Geometric mean graph. In this paper, we investigate Super geometric mean labeling of some union of graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Dual Connected Neighborhood Domination In Graphs[ ]

A subset D ? V (G) of a graph G = (V, E) is said to be dual connected neighborhood domination set of G if D is connected domination set of G and N (G). The dual connected neighborhood domination number is the minimum cardinality taken over all connected neighborhood dominating sets of G and is denoted by?_dcn (G). In this paper, ?_dcn (G) are obtained for some standard graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
THE LEGENDARY DOMINATION NUMBER IN GRAPHS[ ]

A dominating set D of a graph G = (V,E) is said to be a Legendary dominating set of G , if L(G) has a dominating set of cardinality D. The Legendary dominationnumber is the minimum cardinality taken over al Legendary domiunating set of G and is denoted by . In this paper, are obtained for some standard graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Paramount Domination in Bipolar Fuzzy Graphs[ ]

A dominating set D V of a bipolar fuzzy graph BG is said to be paramount dominating set pad-set if V/D is not a dominating set of BG. The minimum cardinality of a pad- set is called paramount domination number of BG and it is denoted by .In this paper some results on paramount domination number are obtained. In this paper, we studied this parameter for connected non complete fuzzy graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Symmetric division deg index of tricyclic and tetracyclic graphs[ ]

The symmetric division deg index (SDD) is one of the 148 discrete Adriatic indices analyzed by Vukc ?ievic ´ and Gas ?perov on the benchmark datasets of the International Academy of Mathematical Chemistry. SDD is a significant predictor of total surface area for polychlorobiphenyls. In this article, we characterize the SDD index for the class of all n-vertex tricyclic and tetra-cyclic graphs.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
The Rebellion Number in Graphs[ ]

A set R?V of a graph G = (V, E) is said to be a ‘rebellion set’ of G, if ¦NR (v) ¦=¦NV\R (v) ¦¦,, v ? R and ¦R ¦ ¦V\R¦. The rebellion number rb (G) is the minimum cardinality of any rebellion set in G. In this paper, we defined rebellion number, strong rebellion number, global rebellion number, total rebellion number for simple graph. Also, we determined its tight bounds for some standard graph and characterize these parameters.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
TENSOR PRODUCT IN DETOUR RADIAL GRAPH[ ]

In this paper, the Tensor Product in Detour Radial graph DR(G) for some standard graphs are determined. Also we introduced b-Radial graph. The maximal energy and minimal energy are defined and they used to find the energy of Tensor Product in Detour Radial graph .

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
An Efficient Routing Method for Lifetime Enhancement in Wireless Sensor Network using Fuzzy Approach[ ]

In recent years, many approaches and techniques have been explored for the optimization of energy usage in wireless sensor networks. Routing is one of these areas in which attempts for efficient utilization of energy have been made. These attempts use fixed (crisp) metrics for making energy-aware routing decisions. In this paper, we present a generalized fuzzy logic based approach for energy-aware routing in wireless sensor net-works. This generalized approach is soft and tunable and hence it can accommodate sensor networks com-prising of different types of sensor nodes having different energy metrics.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
A Systematic Study on Applications of Graph Theory in Image Processing With a Focus on Image Segmentation[ ]

Graph theory has an important role to play in computer science in particular in image processing. Image processing is the process of analysing the digital image by extracting its features and there by classifying it. The output of image processing is an image or set of features of it. The steps of image processing are pre-processing, image segmentation, feature extraction and finally classification. In this paper we have presented systematically how the graph theory is useful in image segmentation and its applications. Also we have used number of graph theoretical concepts which are used in segmenting the digital image.

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------