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Degree Preservable Graphs

R. Anitha, K. Sangavai


The spanning tree of a graph is an important concept in the communication network design and other network related problems. Finding a spanning tree with some additional constraints related to the degree of the vertices, radius or diameter of the graph etc. will find more applications in all networks. In this context we introduce a new spanning tree called v- Degree Preserving Spanning Tree and defined a new family of graphs called Degree Preservable Graphs. In this work it will be proved that the common families of graphs n C and n K , 2 are degree preservable and the families n Q and n W n m where n m K n K , 3 , , _ _ are non-degree preservable. A characterization for bipartite graph in terms of degree preserving nature of the vertices is also presented.


v-degree preserving spanning trees, degree preservable graphs, complete graphs, traceable graphs, bipartite graphs

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